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All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. Write the answer as a quotient of integers. (If necessary, review Section B.2 ). 1110+110011,000+110,0001100,000 In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Monthly payments of $245.65 are made for 4 years to repay a loan at 7.2 compounded monthly In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Semiannual payments of $3,200 are made for 12 years to repay a loan at 9.9 compounded semiannually.In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Quarterly payments of $975 are made for 10 years to repay a loan at 9.9 compounded quarterly.In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Annual payments of $1.045 are made for 5 years to repay a loan at 4.75 compounded annually.In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Semiannual payments of $4,500 are made for 16 years to loan at 8.24 compounded quarterly.In Problems 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Quarterly payments of $610 are made for 6 years to repay loan at 8.24 compounded quarterly.In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Annual payments of $5,195 are made for 9 years to repay a loan at 5.48 compounded annually.In Problem 7-14, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate. Monthly payments of $433 are made for 3 years to repay a loan at 10.8 compounded monthly.In Problems 15-22, use formula 5 or 6 to solve each problem. n=30;i=0.04;PMT=$200;PV=?In Problems 15-22, use formula 5 or 6 to solve each problem. n=40;i=0.01;PMT=$400;PV=?In Problems 15-22, use formula 5 or 6 to solve each problem. PV=$40,000;n=96:i=0.0075;PMT=?In Problems 15-22, use formula 5 or 6 to solve each problem. PV=$14,000;n=72:i=0.005;PMT=?In Problems 15-22, use formula 5 or 6 to solve each problem. PV=$5,000;i=0.01;PMT=$200;n=?In Problems 15-22, use formula 5 or 6 to solve each problem. PV=$20,000;i=0.0175;PMT=$500;n=?In Problems 15-22, use formula 5 or 6 to solve each problem. PV=$9,000;PMT=$600;n=20;i=? (Round answer to three decimal places)In Problems 15-22, use formula 5 or 6 to solve each problem. PV=$12,000;PMT=$400;n=40;i=? (Round answer to three decimal places)Explain what is meant by the present value of an ordinary annuity.Solve the present value formula 5 for n.Explain how an ordinary annuity is involved when you take out an auto loan from a bank.Explain why the last payment m an amortization schedule might differ from the other payments,American General offers a 10 -year ordinary annuity with a guaranteed rate of 6.65 compounded annually. How much should you pay for one of these annuities if you want to receive guaranteed rate of 6.35 compounded annually. How much should you pay for one of these annuities if you want to receive payments of $10,000 annually over the 7-year period?American General offers a 7-year ordinary annuity with a guaranteed rate of 6.35 compounded annually. How much should you pay for one of these annuities if you want to receive payments of $10,000 annually over the 7-year period?E-Loan, an online lending service, offers a 36 -month auto loan at 7.56 compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of 350, how much can you borrow from E-Loan? What is the total interest you will pay for this loan?E-Loan offers a 36 -month auto loan at 9.84 compounded monthly to applicants with fair credit ratings. If you have a fair credit rating and can afford monthly payments of 350, how much can you borrow from E-Loan? What is the total interest you will pay for this loan?If you buy a computer directly from the manufacturer for 2,500 and agree to repay it in 48 equal installments at 1.25 interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?If you buy a computer directly from the manufacturer for 3,500 and agree to repay it in 60 equal installments at 1.75 interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?In Problems 33-36, assume that no new purchases are made with the credit card. The annual interest rate on a credit card is 16.99. If a payment of 100.00 is made each month, how long will it take to pay off an unpaid balance of 2,487.56 ?In Problems 33-36, assume that no new purchases are made with the credit card. The annual interest rate on a credit card is 24.99. If a payment of 100.00 is made each month, how long will it take to pay off an unpaid balance of 2,487.56 ?In Problems 33-36, assume that no new purchases are made with the credit card. The annual interest rate on a credit card is 14.99. If the minimum payment of 20 is made each month, how long will it take to pay off an unpaid balance of 937.14 ?In Problems 33-36, assume that no new purchases are made with the credit card. The annual interest rate on a credit card is 22.99. If the minimum payment of 25 is made each month, how long will it take to pay off an unpaid balance of 860.22 ?Problems 37 and 38 refer to the following ads. The ad for a Bison sedan claims that a monthly payment of $299 constitutes 0 financing. Explain why that is false. Find the annual interest rate compounded monthly that is actually being charged for financing $17,485 with 72 monthly payments of $299.Problems 37 and 38 refer to the following ads. The ad for a Bison sedan claims that a monthly payment of $399 constitutes 0 financing. Explain why that is false. Find the annual interest rate compounded monthly that is actually being charged for financing $23,997 with 72 monthly payments of $399.You want to purchase an automobile for $27,300. The dealer offers you 0 financing for 60 months or a $5,000 rebate. You can obtain 6.3 financing for 60 months at the local bank. Which option should you choose? Explain.You want to purchase an automobile for $28,500. The dealer offers you 0 financing for 60 months or a $6,000 rebate. You can obtain 6.2 financing for 60 months at the local hank. Which option should you choose? Explain.A sailboat costs $35,000. You pay 20 down and amortize the rest with equal monthly payments over a 12-year period. If you must pay 8.75 compounded monthly, what is your monthly payment? How much interest will you pay?A recreational vehicle costs $80,000. You pay 10 down and amortize the rest with equal monthly payments over a 7-year period. If you pay 9.25 compounded monthly, what is your monthly payment? How much interest will you pay?Construct the amortization schedule for a $5,000 debt that is to be amortized in eight equal quarterly payments at 2.8 interest per quarter on the unpaid balance.Construct the amortization schedule for a $10,000 debt that is to be amortized in six equal quarterly payments at 2.6 interest per quarter on the unpaid balance.A woman borrows $6,000 at 9 compounded monthly, which is to be amortized over 3 years in equal monthly payments. For tax purposes, she needs to know the amount of interest paid during each year of the loan. Find the interest paid during the first year, the second year, and the third year of the loan. [Hint: Find the unpaid balance after 12 payments and after 24 payments.]A man establishes an annuity for retirement by depositing $50,000 into an account that pays 7.2 compounded monthly. Equal monthly withdrawals will be made each month for 5 years, at which time the account will have a zero balance. Each year taxes must be paid on the interest earned by the account during that year. How much interest was earned during the first year? [Hint: The amount in the account at the end of the first year is the present value of a 4-year annuity.]Some friends tell you that they paid $25,000 down on a new house and are to pay $525 per month for 30 years. If interest is 7.8 compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?A family is thinking about buying a new house costing $120,000. The family must pay 20 down, and the rest is to be amortized over 30 years in equal monthly payments. If money costs 7.5 compounded monthly, what will the monthly payment be? How much total interest will be paid over 30 years?A student receives a federally backed student loan of $6,000 at 3.5 interest compounded monthly. After finishing college in 2 years, the student must amortize the loan in the next 4 years by making equal monthly payments. What will the payments be and what total interest will the student pay? [Hint: This is a two-part problem. First, find the amount of the debt at the end of the first 2 years: then amortize this amount over the next 4 years.]A person establishes a sinking fund for retirement by contributing $7,500 per year at the end of each year for 20 years. For the next 20 years, equal yearly payments are withdrawn, at the end of which time the account will have a zero balance. If money is worth 9 compounded annually, what yearly payments will the person receive for the last 20 years?A family has a 150,000, 30 -year mortgage at 6.1 compounded monthly. Find the monthly payment. Also find the unpaid balance after A10yearsB20yearsC25years A family has a $210,000, 20-year mortgage at 6.75 compounded monthly. Find the monthly payment. Also find the unpaid balance after A5yearsB10yearsC15years A family has a $129,000, 20-year mortgage at 7.2 compounded monthly. (A) Find the monthly payment and the total interest paid. (B) Suppose the family decides to add an extra $102.41 to its mortgage payment each month starting with the very first payment. How long will it take the family to pay off the mortgage? How much interest will be saved?At the time they retire, a couple has $200,000 in an account that pays 8.4 compounded monthly. (A) If the couple decides to withdraw equal monthly payments for 10 years, at the end of which time the account will have a zero balance, how much should the couple withdraw each month? (B) If the couple decides to withdraw $3,000 a month until the balance in the account is zero, how many withdrawals can the couple make?An ordinary annuity that earns 7.5 compounded monthly has a current balance of $500,000. The owner of the account is about to retire and has to decide how much to withdraw from the account each month. Find the number of withdrawals under each of the following options: A$5,000monthlyB$4,000monthlyC$3,000monthly Refer to Problem 55. If the account owner decides to withdraw $3,000 monthly, how much is in the account after 10 years? After 20 years? After 30 years?An ordinary annuity pays 7.44 compounded monthly. (A) A person deposits $100 monthly for 30 years and then makes equal monthly withdrawals for the next 15 years, reducing the balance to zero. What are the monthly withdrawals? How much interest is earned during the entire 45 -year process? (B) If the person wants to make withdrawals of $2,000 per month for the last 15 years, how much must be deposited monthly for the first 30 years?An ordinary annuity pays 6.48 compounded monthly. (A) A person wants to make equal monthly deposits into the account for 15 years in order to then make equal monthly withdrawals of $1,500 for the next 20 years, reducing the balance to zero. How much should be deposited each month for the first 15 years? What is the total interest earned during this 35 -year process? (B) If the person makes monthly deposits of $1,000 for the first 15years, how much can be withdrawn monthly for the next 20 years?A couple wishes to borrow money using the equity in their home for collateral. A loan company will loan the couple up to 70 of their equity. The couple purchased the home 12 years ago for $179,000. The home was financed by paying 20 down and signing a 30-year mortgage at 8.4 on the unpaid balance. Equal monthly payments were made to amortize the loan over the 30-year period. The net market value of the house is now $215,000. After making the 144th payment, the couple applied to the loan company for the maximum loan. How much (to the nearest dollar) will the couple receive A person purchased a house 10 years ago for $160,000. The house was financed by paying 20 down and signing a 30-year mortgage at 7.75 on the unpaid balance. Equal monthly payments were made to amortize the loan over a 30 -year period. The owner now (after the 120th payment) wishes to refinance the house due to a need for additional cash. If the loan company agrees to a new 30-year mortgage of 80 of the new appraised value of the house, which is $225,000, how much cash (to the nearest dollar) will the owner receive after repaying the balance of the original mortgage?A person purchased a $145,000 home 10 years ago by paying 20 down and signing a 30-year mortgage at 7.9 compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20-year mortgage at 5.5 compounded monthly. How much interest will refinancing save?A person purchased a $200,000 home 20 years ago by paying 20 down and signing a 30-year mortgage at 13.2 compounded monthly. Interest rales have dropped and the owner wants to refinance the unpaid balance by signing a new 10-year mortgage at 8.2 compounded monthly. How much interest will refinancing save?Discuss the similarities and differences in the graphs of unpaid balance as a function of time for 30-year mortgages of $50,000,$75,000,and$100,000, respectively, each at 9 compounded monthly (see the figure). Include computations of the monthly payment and total interest paid in each case.Discuss the similarities and differences in the graphs of unpaid balance as a function of time for 30-year mortgages of $60,000 at rates of 7,10,and13. respectively (see the figure). Include computations of the monthly payment and total interest paid in each case.In Problems solver 65-68, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A discount electronics store offers to let you pay for a $1,000 stereo in 12 equal $90 installments. The store claims that since you repay $1,080 in 1 year, the 80 finance charge represents an 8 annual rate. This would be true if you repaid the loan in a single payment at the end of the year. But since you start repayment after 1 month, this is an amortized loan, and 8 is not the correct rate. What is the annual nominal compounding rate for this loan?In Problems solver 65-68, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A $2,000 computer can be financed by paying $100 per month for 2 years. What is the annual nominal compounding rate for this loan?In Problems solver 65-68, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. The owner of a small business has received two offers of purchase. The first prospective buyer offers to pay the owner $100,000 in cash now. The second offers to pay the owner $10,000 now and monthly payments of $1,200 for 10 years. In effect, the second buyer is asking the owner for a $90,000 loan. If the owner accepts the second offer, what annual nominal compounding rate will the owner receive for financing this purchase?In Problems solver 65-68, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. At the time they retire, a couple has $200,000 invested in an annuity. The couple can take the entire amount in a single payment, or receive monthly payments of $2,000 for 15 years. If the couple elects to receive the monthly payments, what annual nominal compounding rale will the couple earn on the money invested in the annuity?In Problems 1-4, find the indicated quantity, given A=P1+rt. A=?;P=$100;r=9;t=6months In Problems 1-4, find the indicated quantity, given A=P1+rt. A=808;P=?;r=12;t=1month In Problems 1-4, find the indicated quantity, given A=P1+rt. A=212;P=200;r=8;t=?In Problems 1-4, find the indicated quantity, given A=P1+rt. A=$4,120;P=$4,000;r=?;t=6months In Problems 5 and 6, find the indicated quantity, given A=P1+in. A=?;P=$1,200;i=0.005;n=30 In Problems 5 and 6, find the indicated quantity, given A=P1+in. A=$5,000;P=?;i=0.0075;n=60 In Problems 7 and 8, find the indicated quantity, given A=Pert. A=?;P=$4,750;r=6.8;t=3years In Problems 7 and 8, find the indicated quantity, given A=Pert. A=$36,000;P=?;r=9.3;t=60months In Problems 9 and 10, find the indicated quantity, given FV=PMT1+in1i. FV=?;PMT=1,000;i=0.005;n=60 In Problems 9 and 10, find the indicated quantity, given FV=PMT1+in1i. FV=8,000;PMT=?;i=0.015;n=48 In Problems 11 and 12, find the indicated quantity, given PV=PMT11+ini PV=?;PMT=$2,500;i=0.02;n=16 In Problems 11 and 12, find the indicated quantity, given PV=PMT11+ini PV=$8,000;PMT=?;i=0.0075;n=60 Solve the equation 2.500=1.0001.06n for n to the nearest integer using: (A) Logarithms (B) Graphical approximation techniques or an equation solver on a graphing calculator.Solve the equation 5,000=1001.01n10.01 for n to the nearest integer using: (A) Logarithms (B) Graphical approximation techniques or an equation solver on a graphing calculator.If you borrow $3,000 at 14 simple interest for 10 months, how much will you owe in 10 months? How much interest will you pay?Grandpa deposited $6,000 into grandchild’s account toward a college education. How much money (to the nearest dollar) will be in the account 17 years from now if the account earns 7 compounded monthly?How much should you pay for a corporate bond paying 6.6 compounded monthly in order to have $25,000 in 10 years?An investment account pays 5.4 compounded annually. Construct a balance sheet showing the interest earned during each year and the balance at the end of each year for 4 years if (a) A single deposit of $400 is made at the beginning of the first year. (b) Four deposits of $100 are made at the end of each year.One investment pays 13 simple interest and another 9 compounded annually. Which investment would you choose? Why?A $10,000 retirement account is left to earn interest at 7 compounded daily. How much money will be in the account 40 years from now when the owner reaches 65 ? (Use a 365- day year and round answer to the nearest dollar.)A couple wishes to have $40,000 in 6 years for the down payment on a house. At what rate of interest compounded continuously must $25,000 be invested now to accomplish this goal?Which is the better investment and why: 9 compounded quarterly or 9.25 compounded annually?What is the value of an ordinary annuity at the end of 8 years if $200 per month is deposited into an account earning 7.2 compounded monthly? How much of this value is interest?A payday lender charges $60 for a loan of $500 for 15 days. Find the annual interest rate. (Use a 360-day year.)The annual interest rate on a credit card is 25.74 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 30-day billing cycle was $1,672.18. A purchase of $265.12 was made on day 8 and a payment of $250 was credited to the account on day 20. Find the unpaid balance at the end of the billing cycle. (Use a 360-day year.)What will a $23,000 car cost (to the nearest dollar) 5 years from now if the inflation rate over that period averages 5 compounded annually?What would the $23,000 car in Problem 25 have cost (to the nearest dollar) 5 years ago if the inflation rate over that period had averaged 5 compounded annually?A loan of $2,500 was repaid at the end of 10 months with a check for $2,812.50. What annual rate of interest was charged?You want to purchase an automobile for $21,600. The dealer offers you 0 financing for 48 months or a $3,000 rebate. You can obtain 4.8 financing for 48 months at the local bank. Which option should you choose? Explain.Find the annual percentage yield on a bond earning 6.25 if interest is compounded (A) monthly. (B) continuously.You have $5,000 toward the purchase of a boat that will cost $6,000. How long will it take the $5,000 to grow to $6,000 if it is invested at 9 compounded quarterly? (Round up to the next-higher quarter if not exact.)How long will it take money to double if it is invested at 6 compounded monthly? 9 compounded monthly? (Round up to the next-higher month if not exact.)Starting on his 21st birthday, and continuing on every birthday up to and including his 65th, John deposits $2,000 a year into an IRA. How much (to the nearest dollar) will be in the account on John’s 65th birthday, if the account earns: (A) 7 compounded annually? (B) 11 compounded annually?If you just sold a stock for $17,388.17 (net) that cost you $12,903.28 (net) 3 years ago, what annual compound rate of return did you make on your investment?The table shows the fees for refund anticipation loans (RALs) offered by an online tax preparation firm. Find the annual rate of interest for each of the following loans. Assume a 360-day year. (A) A $400 RAL paid back in 15 days (B) A $1,800 RAL paid back in 21 days Lincoln Benefit Life offered an annuity that pays 5.5 compounded monthly. What equal monthly deposit should be made into this annuity in order to have $50,000 in 5 years?A person wants to establish an annuity for retirement purposes. He wants to make quarterly deposits for 20 years so that he can then make quarterly withdrawals of $5,000 for 10 years. The annuity earns 7.32 interest compounded quarterly. (A) How much will have to be in the account at the time he retires? (B) How much should be deposited each quarter for 20 years in order to accumulate the required amount? (C) What is the total amount of interest earned during the 30-year period?If you borrow $4,000 from an online lending firm for the purchase of a computer and agree to repay it in 48 equal installments at 0.9 interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?A company decides to establish a sinking fund to replace a piece of equipment in 6 years at an estimated cost of $50,000. To accomplish this, they decide to make fixed monthly payments into an account that pays 6.12 compounded monthly. How much should each payment be?How long will it lake money to double if it is invested at 7.5 compounded daily? 7.5 compounded annually?A student receives a student loan for $8,000 at 5.5 interest compounded monthly to help her finish the last 1.5 years of college. Starting 1 year after finishing college, the student must amortize the loan in the next 5 years by making equal monthly payments. What will the payments be and what total interest will the student pay?If you invest $5,650 in an account paying 8.65 compounded continuously, how much money will be in the account at the end of 10 years?A company makes a payment of $1,200 each month into a sinking fund that earns 6 compounded monthly. Use graphical approximation techniques on a graphing calculator to determine when the fund will be worth $100,000.A couple has a $50,000, 20-year mortgage at 9 compounded monthly. Use graphical approximation techniques on a graphing calculator to determine when the unpaid balance will drop below $10,000.A loan company advertises in the paper that you will pay only 8 a day for each $100 borrowed. What annual rate of interest are they charging? (Use a 360 day year.)Construct the amortization schedule for a $1,000 debt that is to be amortized in four equal quarterly payments at 2.5 interest per quarter on the unpaid balance.You can afford monthly deposits of only $300 into an account that pays 7.98 compounded monthly. How long will it be until you will have $9,000 to purchase a used car? (Round to the next-higher month if not exact.)A company establishes a sinking fund for plant retooling in 6 years at an estimated cost of850,000. How much should be invested semiannually into an account paying 8.76 compounded semiannually? How much interest will the account earn in the 6 years?49RE If you buy a 13-week T-bill with a maturity value of $5,000 for $4,922.15 from the U.S. Treasury Department, what annual interest rate will you earn?In order to save enough money for the down payment on a condominium, a young couple deposits 200 each month into an account that pays 7.02 interest compounded monthly. If the couple needs 10,000 for a down payment, how many deposits will the couple have to make?A business borrows $80,000 at 9.42 interest compounded monthly for 8 years. (A) What is the monthly payment? (B) What is the unpaid balance at the end of the first year? (C) How much interest was paid during the first year?You unexpectedly inherit $10,000 just after you have made the 72nd monthly payment on a 30-year mortgage of $60,000 at 8.2 compounded monthly. Discuss the relative merits of using the inheritance to reduce the principal of the loan or to buy a certificate of deposit paying 7 compounded monthly.Your parents are considering a $75,000, 30-year mortgage to purchase a new home. The bank at which they have done business for many years offers a rate of 7.54 compounded monthly.A competitor is offering 6.87 compounded monthly. Would it be worthwhile for your parents to switch banks? Explain.How much should a $5,000 face value zero coupon bond, maturing in 5 years, be sold for now, if its rate of return is to be 5.6 compounded annually?If you pay $5,695 for a $10,000 face value zero coupon bond that matures in 10 years, what is your annual compound rate of return?If an investor wants to earn an annual interest rate of 6.4 on a 26-week T-bill with a maturity value of $5,000, how much should the investor pay for the T-bill?Two years ago you borrowed $10,000 at 12 interest compounded monthly, which was to be amortized over 5 years. Now you have acquired some additional funds and decide that you want to pay off this loan. What is the unpaid balance after making equal monthly payments for 2 years?What annual nominal rate compounded monthly has the same annual percentage yield as 7.28 compounded quarterly?(A) A man deposits $2,000 in an IRA on his 21st birthday and on each subsequent birthday up to, and including, his 29th (nine deposits in all). The account earns 8 compounded annually. If he leaves the money in the account without making any more deposits, how much will he have on his 65th birthday, assuming the account continues to earn the same rate of interest? (B) How much would be in the account (to the nearest dollar) on his 65th birthday if he had started the deposits on his 30th birthday and continued making deposits on each birthday until (and including) his 65th birthday?A promissory note will pay $27,000 at maturity 10 years from now. How much money should you be willing to pay now if money is worth 5.5 compounded continuously?In a new housing development, the houses are selling for 100,000 and require a 20 down payment. The buyer is given a choice of 30-year or 15-year financing, both at 7.68 compounded monthly. (A) What is the monthly payment for the 30-year choice? For the 15-year choice? (B) What is the unpaid balance after 10 years for the 30-year choice? For the 15-year choice?A loan company will loan up to 60 of the equity in a home. A family purchased their home 8 years ago for $83,000. The home was financed by paying 20 down and signing a 30-year mortgage at 8.4 for the balance. Equal monthly payments were made to amortize the loan over the 30-year period. The market value of the house is now $95,000. After making the 96th payment, the family applied to the loan company for the maximum loan. How much (to the nearest dollar) will the family receive?A $600 stereo is financed for 6 months by making monthly payments of $110. What is the annual nominal compounding rate for this loan?A person deposits $2,000 each year for 25 years into an IRA. When she retires immediately after making the 25th deposit, the IRA is worth $220,000. (A) Find the interest rate earned by the IRA over the 25-year period leading up to retirement. (B) Assume that the IRA continues to earn the interest rate found in part (A). How long can the retiree withdraw $30,000 per year? How long can she withdraw $24,000 per year?Can a consistent and dependent system have exactly two solutions? Exactly three solutions? Explain.Return to Example 2 and solve each system by substitution. Based on your results, describe how you can recognize a dependent system or an inconsistent system when using substitution.Solve by graphing and check: 2xy=3x+2y=4 Solve each of the following systems by graphing: (a) x+y=42xy=2 (b) 6x3y=92xy=3 (c) 2xy=46x3y=18 Solve to two decimal places using graphical approximation techniques on a graphing calculator: 2x5y=254x+3y=5 Solve by substitution: 3x3y=22xy=6 Solve the following system using elimination by addition: 5x2y=122x+3y=1 Dennis wants to use cottage cheese and yogurt to increase the amount of protein and calcium in his daily diet. An ounce of cottage cheese contains 3 grams of protein and 15 milligrams of calcium. An ounce of yogurt contains 1 gram of protein and 41 milligrams of calcium. How many ounces of cottage cheese and yogurt should Dennis eat each day to provide exactly 62 grams of protein and 760 milligrams of calcium?Find the equilibrium quantity and equilibrium price, and graph the following price-supply and price-demand equations: p=0.08q+0.66Price-supplyequationp=0.1q+3Price-demandequation In Problems 1-6, find the x and y coordinates of the intersection of the given lines. (If necessary, review Section 1.2). y=5x+7andtheyaxis In Problems 1-6, find the x and y coordinates of the intersection of the given lines. (If necessary, review Section 1.2). y=5x+7andthexaxis In Problems 1-6, find the x and y coordinates of the intersection of the given lines. (If necessary, review Section 1.2). 3x+4y=72andthexaxis In Problems 1-6, find the x and y coordinates of the intersection of the given lines. (If necessary, review Section 1.2). 3x+4y=72andtheyaxis In Problems 1-6, find the x and y coordinates of the intersection of the given lines. (If necessary, review Section 1.2). 6x5y=120andx=5 In Problems 1-6, find the x and y coordinates of the intersection of the given lines. (If necessary, review Section 1.2). 6x5y=120andy=3 In Problems 7 and 8, find an equation in point-slope form, yy1=mxx1 of the line through the given points. 2,7and4,5 In Problems 7 and 8, find an equation in point-slope form, yy1=mxx1 of the line through the given points. 3,20and5,4 Match each system in Problems 9-12 with one of the following graphs, and use the graph to solve the system. 4x+2y=82xy=0 Match each system in Problems 9-12 with one of the following graphs, and use the graph to solve the system. x+y=32xy=0 Match each system in Problems 9-12 with one of the following graphs, and use the graph to solve the system. x+2y=52x+3y=3 Match each system in Problems 9-12 with one of the following graphs, and use the graph to solve the system. 2x4y=10x+2y=5 Solve Problem 13-16 by graphing. 3xy=2x+2y=10 Solve Problem 13-16 by graphing. 3x2y=127x+2y=8 Solve Problem 13-16 by graphing. m+2n=42m+4n=8 Solve Problem 13-16 by graphing. 3u+5v=156u+10v=30 Solve Problems 17-20 using substitution. y=2x3x+2y=14 Solve Problems 17-20 using substitution. y=x4x=3y=1 Solve Problems 17-20 using substitution. 2x+y=6xy=3 Solve Problems 17-20 using substitution. 3xy=72x+3y=1 Solve Problems 21-24 using elimination by addition. 3u2v=127u+2v=8 Solve Problems 21-24 using elimination by addition. 2x3y=85x+3y=1 Solve Problems 21-24 using elimination by addition. 2mn=10m2n=4 Solve Problems 21-24 using elimination by addition. 2x+3y=13xy=7 Solve Problems 25-34 using substitution or elimination by addition. 6x2y=45x+3y=8 Solve Problems 25-34 using substitution or elimination by addition. 3x+9y=64x3y=8 Solve Problems 25-34 using substitution or elimination by addition. 4x2y=106x+3y=15 28E Solve Problems 25-34 using substitution or elimination by addition. 4x2y=106x+3y=15 Solve Problems 25-34 using substitution or elimination by addition. 5x+15y=105x15y=10 Solve Problems 25-34 using substitution or elimination by addition. 3m+5n=72m+10n=12 Solve Problems 25-34 using substitution or elimination by addition. 5m7n=92m12n=22 Solve Problems 25-34 using substitution or elimination by addition. x+y=10.3x+0.5y=0.7 Solve Problems 25-34 using substitution or elimination by addition. x+y=10.4x+0.7y=0.1 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. x+0y=70x+y=3 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. x+0y=40x+y=9 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. 5x+0y=40x+3y=2 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. 6x+0y=70x+4y=9 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. x+y=0xy=0 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. 2x+y=05xy=0 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. x2y=40x+y=5 In Problems 35-42, solve the system. Note that each solution can be found mentally, without the use of a calculator or pencil-and paper calculation; try to visualize the graphs of both lines. x+3y=90x+y=2 In a free competitive market, if the supply of a good is greater than the demand, will the price tend to go up or come down?In a free competitive market, if the demand for a good is greater than the supply, will the price tend to go up or come down?Problems 45-48 are concerned with the linear system y=mx+by=nx+c where m,b,nandc are nonzero constants. If the system has a unique solution, discuss the relationships among the four constants.Problems 45-48 are concerned with the linear system y=mx+by=nx+c where m,b,nandc are nonzero constants. If the system has no solution, discuss the relationships among the four constants.Problems 45-48 are concerned with the linear system y=mx+by=nx+c where m,b,nandc are nonzero constants. If the system has an infinite number of solutions, discuss the relationships among the four constants.Problems 45-48 are concerned with the linear system y=mx+by=nx+c where m,b,nandc are nonzero constants. If m=0, how many solutions does the system have?In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y=9x10y=7x+8 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y=5x13y=11x+7 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y=0.2x+0.7y=0.2x0.1 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. y=1.7x+2.3y=1.7x1.3 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. 3x2y=154x+3y=13 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. 3x7y=202x+5y=8 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. 2.4x+3.5y=0.11.7x+2.6y=0.2 In Problems 49-56, use a graphing calculator to find the solution to each system. Round any approximate solutions to three decimal places. 4.2x+5.4y=12.96.4x+3.7y=4.5 In Problems 57-62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect. Is there a point that is a solution to all three equations? x2y=62x+y=8x+2y=2 In Problems 57-62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect. Is there a point that is a solution to all three equations? x+y=3x+3y=153xy=5 In Problems 57-62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect. Is there a point that is a solution to all three equations? x+y=1x2y=83xy=3 In Problems 57-62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect. Is there a point that is a solution to all three equations? xy=6x2y=8x+4y=4 In Problems 57-62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect. Is there a point that is a solution to all three equations? 4x3y=242x+3y=128x6y=24 In Problems 57-62, graph the equations in the same coordinate system. Find the coordinates of any points where two or more lines intersect. Is there a point that is a solution to all three equations? 2x+3y=182x6y=64x+6y=24 The coefficients of the three systems given below are similar. One might guess that the solution sets to the three systems would be nearly identical. Develop evidence for or against this guess by considering graphs of the systems and solutions obtained using substitution or elimination by addition. A5x+4y=411x+9y=4 B5x+4y=411x+8y=4 C5x+4y=410x+8y=4 Repeat Problem 63 for the following systems: A6x5y=10(B)6x5y=1013+11y=2011x+8y=4C6x5y=1012x+10y=20 bushels, and the annual demand is 2.0 billion bushels. When the price increases to $5.10 per bushel, the annual supply in-creases to 2.1 billion bushels, and the annual demand decreases to 1.8 billion bushels. Assume that the price-supply and price-demand equations are linear. (A) Find the price-supply equation. (B) Find the price-demand equation. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.Supply and demand for T-shirts. Suppose that the supply and demand equations for printed T-shirts for a particular week are p=0.7q+3Price-supplyequationp=1.7q+15Price-demandequation where p is the price in dollars and q is the quantity in hundreds. (A) Find the supply and demand (to the nearest unit) if T-shirts are $4 each. Discuss the stability of the T-shirt market at this price level. (B) Find the supply and demand (to the nearest unit) if T-shirts are $9 each. Discuss the stability of the T-shirt market at this price level. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.Supply and demand for baseball caps. Suppose that the supply and demand for printed baseball caps for a particular week are p=0.4q+3.2Price-supplyequationp=1.97q+17Price-demandequation where p is the price in dollars and q is the quantity in hundreds. (A) Find the supply and demand (to the nearest unit) if baseball caps are $4 each. Discuss the stability of the baseball cap market at this price level. (B) Find the supply and demand (to the nearest unit) if baseball caps are $9 each. Discuss the stability of the baseball cap market at this price level. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.Supply and demand for soybeans. At $4.80 per bushel, the annual supply for soybeans in the Midwest is 1.9 billion bushels, and the annual demand is 2.0 billion bushels. When the price increases to $5.10 per bushel, the annual supply in-creases to 2.1 billion bushels, and the annual demand decreases to 1.8 billion bushels. Assume that the price-supply and price-demand equations are linear. (A) Find the price-supply equation. (B) Find the price-demand equation. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.Supply and demand for corn. At $2.13 per bushel, the annual supply for corn in the Midwest is 8.9 billion bushels and the annual demand is 6.5 billion bushels. When the price falls to $1.50 per bushel, the annual supply decreases to 8.2 billion bushels and the annual demand increases to 7.4 billion bushels. Assume that the price-supply and price-demand equations are linear. (A) Find the price-supply equation. (B) Find the price-demand equation. (C) Find the equilibrium price and quantity. (D) Graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve.Break-even analysis. A small plant manufactures riding lawn mowers. The plant has fixed costs (leases, insurance, etc.) of $48,000 per day and variable costs (labor, materials, etc.) of $48,000 per unit produced. The mowers are sold for $1,800 each. So the cost and revenue equations are y=48,000+1,400xCostequationy=1,800xRevenueequation where x is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars. (A) How many units must be manufactured and sold each day for the company to break even? (B) Graph both equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.Break-even analysis. Repeat Problem 69 with the cost and revenue equations y=65,000+1,100xCostequationy=1,600xRevenueequation Break-even analysis. A company markets exercise DVDs that sell for $19.95, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $24,000 and the variable costs (materials, shipping, etc) are $7.45 per DVD. (A) Find the cost equation and the revenue equation. (B) How many DVDs must be sold each month for the company to break even? (C) Graph the cost and revenue equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.Break-even analysis. Repeat Problem 71 if the monthly fixed costs increase to $27,200, the variable costs increase to $9.15 and the company raises the selling price of the DVDs to $21.95.Delivery charges. United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing I pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $27.75 for shipping a 5-pound package and $64.50 for a 20-pound package. Find the base price and the surcharge for each additional pound.Delivery charges. Refer to Problem 73. Federated Shipping, a competing overnight delivery service, informs the customer in Problem 73 that they would ship the 5 -pound package for $29.95 and the 20 -pound package for $59.20. (A) If Federated Shipping computes its cost in the same manner as United Express, find the base price and the surcharge for Federated Shipping. (B) Devise a simple rule that the customer can use to choose the cheaper of the two services for each package shipped. Justify your answer.Coffee blends. A coffee company uses Colombian and Brazilian coffee beans to produce two blends, robust and mild. A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. Coffee is shipped in 132 -pound burlap bags. The company has 50 bags of Colombian beans and 40 bags of Brazilian beans on hand. How many pounds of each blend should the company produce in order to use all the available beans?Coffee blends. Refer to Problem 75. (A) If the company decides to discontinue production of the robust blend and produce only the mild blend, how many pounds of the mild blend can the company produce? How many beans of each type will the company use? Are there any beans that arc not used? (B) Repeat part (A) if the company decides to discontinue production of the mild blend and produce only the robust blend.Animal diet. Animals in an experiment are to be kept under a strict diet. Each animal should receive 20 grams of protein and 6 grams of fat. The laboratory technician is able to purchase two food mixes: Mix A has 10 protein and 6 fat; mix B has 20 protein and 2 fat. How many grams of each mix should be used to obtain the right diet for one animal?Fertilizer. A fruit grower uses two types of fertilizer in an orange grove, brand A and brand B. Each bag of brand A contains 8 pounds of nitrogen and 4 pounds of phosphoric acid. Each bag of brand B contains 7 pounds of nitrogen and 6 pounds of phosphoric acid. Tests indicate that the grove needs 720 pounds of nitrogen and 500 pounds of phosphoric acid. How many bags of each brand should be used to provide the required amounts of nitrogen and phosphoric acid?Electronics. A supplier for the electronics industry manufactures keyboards and screens for graphing calculators at plants in Mexico and Taiwan. The hourly production rates at each plant are given in the table. How many hours should each plant be operated to exactly fill an order for 4,000 keyboards and 4,000 screens?Sausage. A company produces Italian sausages and bratwursts at plants in Green Bay and Sheboygan. The hourly production rates at each plant are given in the table. How many hours should each plant operate to exactly fill an order for 62.250 Italian sausages and 76,500 bratwursts?Physics. An object dropped off the top of a tall building falls vertically with constant acceleration. If s is the distance of the object above the ground (in feet) t seconds after its release, then s and t are related by an equation of the form s=a+bt2 where a and b are constants. Suppose the object is 180 feet above the ground 1 second after its release and 132 feet above the ground 2 seconds after its release. (A) Find the constants aandb. (B) How tall is the building? (C) How long does the object fall?Physics. Repeat Problem 81 if the object is 240 feet above the ground after 1 second and 192 feet above the ground after 2 seconds.Earthquakes. An earthquake emits a primary wave and a secondary wave. Near the surface of the Earth the primary wave travels at 5 miles per second and the secondary wave at 3 miles per second. From the time lag between the two waves arriving at a given receiving station, it is possible to estimate the distance to the quake. Suppose a station measured a time difference of 16 seconds between the arrival of the two waves. How long did each wave travel, and how far was the earthquake from the station?Sound waves. A ship using sound-sensing devices above and below water recorded a surface explosion 6 seconds sooner by its underwater device than its above-water device. Sound travels in air at 1,100 feet per second and in seawater at 5,000 feet per second. How long did it take each sound wave to reach the ship? How far was the explosion from the ship?Psychology. People approach certain situations with "mixed emotions." For example, public speaking often brings forth the positive response of recognition and the negative response of failure. Which dominates? J. S. Brown, in an experiment on approach and avoidance, trained rats by feeding them from a goal box. The rats received mild electric shocks from the same goal box. This established an approach-avoidance conflict relative to the goal box. Using an appropriate apparatus. Brown arrived at the following relationships: p=15d+70Approachequationp=43d+230Avoidanceequation where 30d172.5. The approach equation gives the pull (in grams) toward the food goal box when the rat is placed d centimeters away from it. The avoidance equation gives the pull (in grams) away from the shock goal box when the rat is placed d centimeters from it. (A) Graph the approach equation and the avoidance equation in the same coordinate system. (B) Find the value of d for the point of intersection of these two equations. (C) What do you think the rat would do when placed the distance d from the box found in part (B)?The summary following the solution of Example 1 shows five augmented matrices. Write the linear system that each matrix represents, solve each system graphically, and discuss the relationships among these solutions.The solution of Example 3 involved three augmented matrices. Write the linear system that each matrix represents, solve each system graphically, and discuss the relationships among these solutions.Solve using augmented matrix methods: 2x1x2=7 Solve using augmented matrix methods: 5x12x2=112x1+3x2=52 Solve using augmented matrix methods: 2x1+6x2=63x19x2=9 Solve using augmented matrix methods: 2x1x2=34x12x2=1 Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 How many elements are there in A ? In C ?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 How many elements are there in B ? In D ?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 What is the size of B ? of D ?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 What is the size of A ? Of C ?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 Which of the matrices is a column matrix?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 Which of the matrices is a row matrix?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 Which of the matrices is a square matrix?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 Which of the matrices does not contain the element 0 ?Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 List the elements on the principal diagonal of A.Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 List the elements on the principal diagonal of B.Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 For matrix B, list the elements b31,b22,b13.Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 For matrix A, list the elements a21,a12.Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 For matrix C, find c11+c12+c13.Problems 1-14 refer to the following matrices: (If necessary, review the terminology at the beginning of Section 4.2.) A=240615B=190487240C=230D=58 For matrix D,findd11+d21.In Problems 15-18, write the coefficient matrix and the augmented matrix of the given system of linear equations. 3x1+5x2=82x14x2=7 In Problems 15-18, write the coefficient matrix and the augmented matrix of the given system of linear equations. 8x1+3x2=106x1+5x2=13 In Problems 15-18, write the coefficient matrix and the augmented matrix of the given system of linear equations. x1+4x2=156x1=18 In Problems 15-18, write the coefficient matrix and the augmented matrix of the given system of linear equations. 5x1x2=103x2=21 In Problems 19-22, write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2. 251479 In Problems 19-22, write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2. 03821525 In Problems 19-22, write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2. 40081040 In Problems 19-22, write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2. 1201126 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 R1R2 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 R2R1 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 2R2R2 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 2R2R2 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 R1+R2R1 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 R1+R2R2 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 12R1R1 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 12R1R1 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 1R2+R1R1 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 2R2+R1R1 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 1R1+R2R2 Perform the row operations indicated in Problems 23-34 on the following matrix: 241365 12R1+R2R2 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 122134 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 2463612 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 120936 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 3063512 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 1163112 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 122530 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 6312123 Each of the matrices in Problems 35-42 is the result of performing a single row operation on the matrix A shown below. Identify the row operation. A=1263312 120936 Solve Problems 43-46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system's solution set. 3x12x2=64x13x2=6 Solve Problems 43-46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system's solution set. x12x2=52x1+4x2=10 Solve Problems 43-46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system's solution set. 3x12x2=36x1+4x2=6 Solve Problems 43-46 using augmented matrix methods. Graph each solution set. Discuss the differences between the graph of an equation in the system and the graph of the system's solution set. x12x2=12x1+5x2=2 Solve Problems 47 and 48 using augmented matrix methods. Write the linear system represented by each augmented matrix in your solution, and solve each of these systems graphically. Discuss the relationships among the solutions of these systems. x1+x2=5x1x2=1 Solve Problems 47 and 48 using augmented matrix methods. Write the linear system represented by each augmented matrix in your solution, and solve each of these systems graphically. Discuss the relationships among the solutions of these systems. x1x2=2x1+x2=6 Each of the matrices in Problems 49-54 is the final matrix form for a system of two linear equations in the variables x1 and x2 Write the solution of the system. 100146 Each of the matrices in Problems 49-54 is the final matrix form for a system of two linear equations in the variables x1 and x2 Write the solution of the system. 100135 Each of the matrices in Problems 49-54 is the final matrix form for a system of two linear equations in the variables x1 and x2 Write the solution of the system. 130024 Each of the matrices in Problems 49-54 is the final matrix form for a system of two linear equations in the variables x1 and x2 Write the solution of the system. 120079 Each of the matrices in Problems 49-54 is the final matrix form for a system of two linear equations in the variables x1 and x2 Write the solution of the system. 1200150 Each of the matrices in Problems 49-54 is the final matrix form for a system of two linear equations in the variables x1 and x2 Write the solution of the system. 1500100 Solve Problems 55-74 using augmented matrix methods: x12x2=12x1x2=5 Solve Problems 55-74 using augmented matrix methods: x1+3x2=13x12x2=14 Solve Problems 55-74 using augmented matrix methods: x14x2=22x1+x2=3 Solve Problems 55-74 using augmented matrix methods: x14x2=53x1x2=5 Solve Problems 55-74 using augmented matrix methods: 3x1x2=2x1+2x2=10 Solve Problems 55-74 using augmented matrix methods: 2x1+x2=0x12x2=5 Solve Problems 55-74 using augmented matrix methods: x1+2x2=42x1+4x2=8 Solve Problems 55-74 using augmented matrix methods: 2x1+3x2=24x1+6x2=7 Solve Problems 55-74 using augmented matrix methods: 2x1+x2=6x1x2=3 Solve Problems 55-74 using augmented matrix methods: 3x1x2=5x1+3x2=5 Solve Problems 55-74 using augmented matrix methods: 3x16x2=92x1+4x2=6 Solve Problems 55-74 using augmented matrix methods: 2x14x2=23x1+6x2=3 Solve Problems 55-74 using augmented matrix methods: 4x1+2x2=26x1+3x2=3 Solve Problems 55-74 using augmented matrix methods: 6x1+2x2=43x1x2=2 Solve Problems 55-74 using augmented matrix methods: 2x1+x2=14x1x2=7 Solve Problems 55-74 using augmented matrix methods: 2x1x2=82x1+x2=8 Solve Problems 55-74 using augmented matrix methods: 4x16x2=86x1+9x2=10 Solve Problems 55-74 using augmented matrix methods: 2x14x2=43x1+6x2=4

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