Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Algebra
Without graphing, determine the number of solutions and then classify the system of equations. {y=2x44x+2y=9Without graphing, determine the number of solutions and then classify the system of equations. {y= 1 3x5x3y=6Without graphing, determine the number of solutions and then classify the system of equations. {3x+2y=22x+y=1Without graphing, determine the number of solutions and then classify the system of equations. {x+4y=12x+y=3Without graphing, determine the number of solutions and then classify the system of equations. {4x5y=20y= 4 5x4Without graphing, determine the number of solutions and then classify the system of equations. {2x4y=8y= 1 2x2Manny is making 12 quarts of orange juice from concentrate and water. The number of quarts of water is 3 times the number of quarts of concentrate. How many quarts of concentrate and how many quarts of water does Manny need?Alisha is making an 18 ounce coffee beverage that is made from brewed coffee and milk. The number of ounces of brewed coffee is 5 times greater than the number of ounces of milk. How many ounces of coffee and how many ounces of milk does Alisha need?In the following exercises, determine if the following points are solutions to the given system of equations. 1. {2x6y=03x4y=5 (a) (3,1) (b) (3,4)In the following exercises, determine if the following points are solutions to the given system of equations. 2. {7x4y=13x2y=1 (a) (b) (1,2)In the following exercises, determine if the following points are solutions to the given system of equations. 3. {2x+y=5x+y=1 (a) (4,3) (b) (2,0)In the following exercises, determine if the following points are solutions to the given system of equations. 4. {3x+y=8x+2y=9 (a) (5,7) (b) (5,7)In the following exercises, determine if the following points are solutions to the given system of equations. 5. {x+y=2y= 3 4x (a) (87,67) (b) (1,34)In the following exercises, determine if the following points are solutions to the given system of equations. 6. {x+y=1y= 2 5x (a) (57,27) (b) (5,2)In the following exercises, determine if the following points are solutions to the given system of equations. 7. {x+5y=10y= 3 5x+1 (a) (10,4) (b) (54,74)In the following exercises, determine if the following points are solutions to the given system of equations. 8. {x+3y=9y= 2 3x2 (a) (6,5) (b) (5,43)In the following exercises, solve the following systems of equations by graphing. 9. {3x+y=32x+3y=5In the following exercises, solve the following systems of equations by graphing. 10. {x+y=22x+y=4In the following exercises, solve the following systems of equations by graphing. 11. {3x+y=12x+y=4In the following exercises, solve the following systems of equations by graphing. 12. {2x+3y=3x+y=4In the following exercises, solve the following systems of equations by graphing. 13. {y=x+2y=2x+2In the following exercises, solve the following systems of equations by graphing. 14. {y=x2y=3x+2In the following exercises, solve the following systems of equations by graphing. 15. {y= 3 2x+1y= 1 2x+5In the following exercises, solve the following systems of equations by graphing. 16. {y= 2 3x2y= 1 3x5In the following exercises, solve the following systems of equations by graphing. 17. {x+y=34x+4y=4In the following exercises, solve the following systems of equations by graphing. 18. {xy=32xy=4In the following exercises, solve the following systems of equations by graphing. 19. {3x+y=12x+y=4In the following exercises, solve the following systems of equations by graphing. 20. {3x+y=24x2y=6In the following exercises, solve the following systems of equations by graphing. 21. {x+y=52xy=4In the following exercises, solve the following systems of equations by graphing. 22. {xy=22xy=6In the following exercises, solve the following systems of equations by graphing. 23. {x+y=2xy=0In the following exercises, solve the following systems of equations by graphing. 24. {x+y=6xy=8In the following exercises, solve the following systems of equations by graphing. 25. {x+y=5xy=3In the following exercises, solve the following systems of equations by graphing. 26. {x+y=4xy=0In the following exercises, solve the following systems of equations by graphing. 27. {x+y=4x+2y=2In the following exercises, solve the following systems of equations by graphing. 28. {x+3y=3x+3y=3In the following exercises, solve the following systems of equations by graphing. 29. {2x+3y=3x+3y=12In the following exercises, solve the following systems of equations by graphing. 30. {2xy=42x+3y=12In the following exercises, solve the following systems of equations by graphing. 31. {2x+3y=6y=2In the following exercises, solve the following systems of equations by graphing. 32. {2x+y=2y=4In the following exercises, solve the following systems of equations by graphing. 33. {x3y=3y=2In the following exercises, solve the following systems of equations by graphing. 34. {2x2y=8y=3In the following exercises, solve the following systems of equations by graphing. 35. {2xy=1x=1In the following exercises, solve the following systems of equations by graphing. 36. {x+2y=2x=2In the following exercises, solve the following systems of equations by graphing. 37. {x3y=6x=3In the following exercises, solve the following systems of equations by graphing. 38. {x+y=4x=1In the following exercises, solve the following systems of equations by graphing. 39. {4x3y=88x6y=14In the following exercises, solve the following systems of equations by graphing. 40. {x+3y=42x6y=3In the following exercises, solve the following systems of equations by graphing. 41. {2x+4y=4y= 1 2xIn the following exercises, solve the following systems of equations by graphing. 42. {3x+5y=10y= 3 5x+1In the following exercises, solve the following systems of equations by graphing. 43. {x=3y+42x+6y=8In the following exercises, solve the following systems of equations by graphing. 44. {4x=3y+78x6y=14In the following exercises, solve the following systems of equations by graphing. 45. {2x+y=68x4y=24In the following exercises, solve the following systems of equations by graphing. 46. {5x+2y=710x4y=14In the following exercises, solve the following systems of equations by graphing. 47. {x+3y=64y= 4 3x8In the following exercises, solve the following systems of equations by graphing. 48. {x+2y=6y= 1 2x1In the following exercises, solve the following systems of equations by graphing. 49. {3x+2y=2y=x+4In the following exercises, solve the following systems of equations by graphing. 50. {x+2y=2y=x1Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 51. {y= 2 3x+12x+3y=5Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 52. {y= 1 3x+2x3y=9Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 53. {y=2x+14x+2y=8Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 54. {y=3x+49x3y=18Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 55. {y= 2 3x+12x3y=7Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 56. {3x+4y=12y=3x1Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 57. {4x+2y=104x2y=6Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 58. {5x+3y=42x3y=5Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 59. {y= 1 2x+5x+2y=10Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 60. {y=x+1x+y=1Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 61. {y=2x+32xy=3Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. 62. {5x2y=10y= 5 2x5In the following exercises, solve. 63. Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water. How many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water?In the following exercises, solve. 64. Jamal is making a snack mix that contains only pretzels and nuts. For every ounce of nuts, he will use 2 ounces of pretzels. How many ounces of pretzels and how many ounces of nuts does he need to make 45 ounces of snack mix?In the following exercises, solve. 65. Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?In the following exercises, solve. 66. Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?Leo is planning his spring flower garden. He wants to plant tulip and daffodil bulbs. He will plant 6 times as many daffodil bulbs as tulip bulbs. If he wants to plant 350 bulbs, how many tulip bulbs and how many daffodil bulbs should he plant?A marketing company surveys 1,200 people. They surveyed twice as many females as males. How many males and females did they survey?In a system of linear equations, the two equations have the same slope. Describe the possible solutions to the system.In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.Solve the system by substitution. {2x+y=11x+3y=9Solve the system by substitution. {x+3y=104x+y=18Solve the system by substitution. {x+y=6y=3x2Solve the system by substitution. {2xy=1y=3x6Solve the system by substitution. {4x+y=23x+2y=1Solve the system by substitution. {x+y=44xy=2Solve the system by substitution. {x5y=134x3y=1Solve the system by substitution. {x6y=62x4y=4Solve the system by substitution. {y=3x16y= 1 3xSolve the system by substitution. {y=x+10y= 1 4xSolve the system by substitution. {x4y=43x+4y=0Solve the system by substitution. {4xy=02x3y=5Solve the system by substitution. {2x3y=1212y+8x=48Solve the system by substitution. {5x+2y=124y10x=24Solve the system by substitution. {3x+2y=9y= 3 2x+1Solve the system by substitution. {5x3y=2y= 5 3x4The sum of two numbers is 10. One number is 4 less than the other. Find the numbers.The sum of two number is 6 . One number is 10 less than the other. Find the numbers.The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length and width of the rectangle.The perimeter of a rectangle is 58. The length is 5 more than three times the width. Find the length and width of the rectangle.The measure of one of the small angles of a right triangle is 2 more than 3 times the measure of the other small angle. Find the measure of both angles.The measure of one of the small angles of a right triangle is 18 less than twice the measure of the other small angle. Find the measure of both angles.Geraldine has been offered positions by two insurance companies. The first company pays a salary of $12,000 plus a commission of $100 for each policy sold. The second pays a salary of $20,000 plus a commission of $50 for each policy sold. How many policies would need to be sold to make the total pay the same?Kenneth currently sells suits for company A at a salary of $22,000 plus a $10 commission for each suit sold. Company B offers him a position with a salary of $28,000 plus a $4 commission for each suit sold. How many suits would Kenneth need to sell for the options to be equal?In the following exercises, solve the systems of equations by substitution. 71. {2x+y=43x2y=6In the following exercises, solve the systems of equations by substitution. 72. {2x+y=23xy=7In the following exercises, solve the systems of equations by substitution. 73. {x2y=52x3y=4In the following exercises, solve the systems of equations by substitution. 74. {x3y=92x+5y=4In the following exercises, solve the systems of equations by substitution. 75. {5x2y=6y=3x+3In the following exercises, solve the systems of equations by substitution. 76. {2x+2y=6y=3x+1In the following exercises, solve the systems of equations by substitution. 77. {2x+3y=3y=x+3In the following exercises, solve the systems of equations by substitution. 78. {2x+5y=14y=2x+2In the following exercises, solve the systems of equations by substitution. 79. {2x+5y=1y= 1 3x2In the following exercises, solve the systems of equations by substitution. 80. {3x+4y=1y= 2 5x+2In the following exercises, solve the systems of equations by substitution. 81. {3x2y=6y= 2 3x+2In the following exercises, solve the systems of equations by substitution. 82. {3x5y=3y= 1 2x5In the following exercises, solve the systems of equations by substitution. 83. {2x+y=10x+y=5In the following exercises, solve the systems of equations by substitution. 84. {2x+y=10x+2y=16In the following exercises, solve the systems of equations by substitution. 85. {3x+y=14x+y=15In the following exercises, solve the systems of equations by substitution. 86. {x+y=02x+3y=4In the following exercises, solve the systems of equations by substitution. 87. {x+3y=13x+5y=5In the following exercises, solve the systems of equations by substitution. 88. {x+2y=12x+3y=1In the following exercises, solve the systems of equations by substitution. 89. {2x+y=5x2y=15In the following exercises, solve the systems of equations by substitution. 90. {4x+y=10x2y=20In the following exercises, solve the systems of equations by substitution. 91. {y=2x1y= 1 3x+4In the following exercises, solve the systems of equations by substitution. 92. {y=x6y= 3 2x+4In the following exercises, solve the systems of equations by substitution. 93. {y=2x8y= 3 5x+6In the following exercises, solve the systems of equations by substitution. 94. {y=x1y=x+7In the following exercises, solve the systems of equations by substitution. 95. {4x+2y=88xy=1In the following exercises, solve the systems of equations by substitution. 96. {x12y=12x8y=6In the following exercises, solve the systems of equations by substitution. 97. {15x+2y=65x+2y=4In the following exercises, solve the systems of equations by substitution. 98. {2x15y=712x+2y=4In the following exercises, solve the systems of equations by substitution. 99. {y=3x6x2y=0In the following exercises, solve the systems of equations by substitution. 100. {x=2y4x8y=0In the following exercises, solve the systems of equations by substitution. 101. {2x+16y=8x8y=4In the following exercises, solve the systems of equations by substitution. 102. {15x+4y=630x8y=12In the following exercises, solve the systems of equations by substitution. 103. {y=4x4x+y=1In the following exercises, solve the systems of equations by substitution. 104. {y= 1 4xx+4y=8In the following exercises, solve the systems of equations by substitution. 105. {y= 7 8x+47x+8y=6In the following exercises, solve the systems of equations by substitution. 106. {y= 2 3x+52x+3y=11In the following exercises, translate to a system of equations and solve. 107. The sum of two numbers is 15. One number is 3 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 108. The sum of two numbers is 30. One number is 4 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 109. The sum of two numbers is 26 . One number is 12 less than the other. Find the numbers.In the following exercises, translate to a system of equations and solve. 110. The perimeter of a rectangle is 50. The length is 5 more than the width. Find the length and width.In the following exercises, translate to a system of equations and solve. 111. The perimeter of a rectangle is 60. The length is 10 more than the width. Find the length and width.In the following exercises, translate to a system of equations and solve. 112. The perimeter of a rectangle is 58. The length is 5 more than three times the width. Find the length and width.In the following exercises, translate to a system of equations and solve. 113. The perimeter of a rectangle is 84. The length is 10 more than three times the width. Find the length and width.In the following exercises, translate to a system of equations and solve. 114. The measure of one of the small angles of a right triangle is 14 more than 3 times the measure of the other small angle. Find the measure of both angles.In the following exercises, translate to a system of equations and solve. 115. The measure of one of the small angles of a right triangle is 26 more than 3 times the measure of the other small angle. Find the measure of both angles.In the following exercises, translate to a system of equations and solve. 116. The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.In the following exercises, translate to a system of equations and solve. 117. The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles.In the following exercises, translate to a system of equations and solve. 118. Maxim has been offered positions by two car dealers. The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold. The second pays a salary of $20,000 plus a commission of $500 for each car sold. How many cars would need to be sold to make the total pay the same?In the following exercises, translate to a system of equations and solve. 119. Jackie has been offered positions by two cable companies. The first company pays a salary of $ 14,000 plus a commission of $100 for each cable package sold. The second pays a salary of $20,000 plus a commission of $25 for each cable package sold. How many cable packages would need to be sold to make the total pay the same?In the following exercises, translate to a system of equations and solve. 120. Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?In the following exercises, translate to a system of equations and solve. 121. Mitchell currently sells stoves for company A at a salary of $12,000 plus a $150 commissionfor each stove he sells. Company Boffers him a position with a salary of $24,000 plus a $50 commission for each stove he sells. How many stoves would Mitchell need to sell for the options to be equal?When Gloria spent 15 minutes on the elliptical trainer and then did circuit training for 30 minutes, her fitness app says she burned 435 calories. When she spent 30 minutes on the elliptical trainer and 40 minutes circuit training she burned 690 calories. Solve the system {15e+30c=43530e+40c=690 for e, the number of calories she burns for each minute on the elliptical trainer, and c, the number of calories she burns for each minute of circuit training.Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56 miles per hour. Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour. Solve the system {56s=70ts=t+ 1 2 . (a)fort to find out how long it will take Tina to catch up to Stephanie. (b)what is the value of s, the number of hours Stephanie will have driven before Tina catches up to her?Solve the system of equations {x+y=10xy=6 (a)by graphing. (b)by substitution. (c) Which method do you prefer? Why?Solve the system of equations {3x+y=12x=y8 by substitution and explain all your steps in words.Solve the system by elimination. {3x+y=52x3y=7Solve the system by elimination. {4x+y=52x2y=2Solve the system by elimination. {2x+y=5xy=4Solve the system by elimination. {x+y=32xy=1Solve the system by elimination. {4x3y=15x9y=4Solve the system by elimination. {3x+2y=26x+5y=8Solve the system by elimination. {3x4y=95x+3y=14Solve the system by elimination. {7x+8y=43x5y=27Solve the system by elimination. { 1 3x 1 2y=1 3 4xy= 5 2Solve the system by elimination. {x+ 3 5y= 1 5 1 2x 2 3y= 5 6Solve the system by elimination. {5x3y=15y=5+ 5 3xSolve the system by elimination. {x+2y=6y= 1 2x+3Solve the system by elimination. {3x+2y=89x6y=13Solve the system by elimination. {7x3y=214x+6y=8The sum of two numbers is 42. Their difference is 8. Find the numbers.The sum of two numbers is 15 . Their difference is 35 . Find the numbers.Malik stops at the grocery store to buy a bag of diapers and 2 cans of formula. He spends a total of $37. The next week he stops and buys 2 bags of diapers and 5 cans of formula for a total of $87. How much does a bag of diapers cost? How much is one can of formula?To get her daily intake of fruit for the day, Sasha eats a banana and 8 strawberries on Wednesday for a calorie count of 145. On the following Wednesday, she eats two bananas and 5 strawberries for a total of 235 calories for the fruit. How many calories are there in a banana? How many calories are in a strawberry?For each system of linear equations, decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. (a) {4x5y=323x+2y=1 (b) {x=2y13x5y=7For each system of linear equations, decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. (a) {y=2x13x4y=6 (b) {6x2y=123x+7y=13In the following exercises, solve the systems of equations by elimination. 126. {5x+2y=23xy=0In the following exercises, solve the systems of equations by elimination. 127. {3x+y=9x2y=12In the following exercises, solve the systems of equations by elimination. 128. {6x5y=12x+y=13In the following exercises, solve the systems of equations by elimination. 129. {3xy=74x+2y=6In the following exercises, solve the systems of equations by elimination. 130. {x+y=1xy=5In the following exercises, solve the systems of equations by elimination. 131. {x+y=8xy=6In the following exercises, solve the systems of equations by elimination. 132. {3x2y=1x+2y=9In the following exercises, solve the systems of equations by elimination. 133. {7x+6y=10x6y=22In the following exercises, solve the systems of equations by elimination. 134. {3x+2y=3x2y=19In the following exercises, solve the systems of equations by elimination. 135. {5x+2y=15x4y=7In the following exercises, solve the systems of equations by elimination. 136. {6x+4y=46x5y=8In the following exercises, solve the systems of equations by elimination. 137. {3x4y=11x2y=5In the following exercises, solve the systems of equations by elimination. 138. {5x7y=29x+3y=3In the following exercises, solve the systems of equations by elimination. 139. {6x5y=75x2y=13In the following exercises, solve the systems of equations by elimination. 140. {x+4y=83x+5y=10In the following exercises, solve the systems of equations by elimination. 141. {2x5y=73xy=17In the following exercises, solve the systems of equations by elimination. 142. {5x3y=12xy=2In the following exercises, solve the systems of equations by elimination. 143. {7x+y=413x+3y=4In the following exercises, solve the systems of equations by elimination. 144. {3x+5y=132x+y=26In the following exercises, solve the systems of equations by elimination. 145. {3x5y=95x+2y=16In the following exercises, solve the systems of equations by elimination. 146. {4x3y=32x+5y=31In the following exercises, solve the systems of equations by elimination. 147. {4x+7y=142x+3y=32In the following exercises, solve the systems of equations by elimination. 148. {5x+2y=217x4y=9In the following exercises, solve the systems of equations by elimination. 149. {3x+8y=32x+5y=3In the following exercises, solve the systems of equations by elimination. 150. {11x+9y=57x+5y=1In the following exercises, solve the systems of equations by elimination. 151. {3x+8y=675x+3y=60In the following exercises, solve the systems of equations by elimination. 152. {2x+9y=43x+13y=7In the following exercises, solve the systems of equations by elimination. 153. { 1 3xy=3x+ 5 2y=2In the following exercises, solve the systems of equations by elimination. 154. {x+ 1 2y= 3 2 1 5x 1 5y=3In the following exercises, solve the systems of equations by elimination. 155. {x+ 1 3y=1 1 2x 1 3y=2In the following exercises, solve the systems of equations by elimination. 156. { 1 3xy=3 2 3x+ 5 2y=3In the following exercises, solve the systems of equations by elimination. 157. {2x+y=36x+3y=9In the following exercises, solve the systems of equations by elimination. 158. {x4y=13x+12y=3In the following exercises, solve the systems of equations by elimination. 159. {3xy=86x+2y=16In the following exercises, solve the systems of equations by elimination. 160. {4x+3y=220x+15y=10In the following exercises, solve the systems of equations by elimination. 161. {3x+2y=66x4y=12In the following exercises, solve the systems of equations by elimination. 162. {5x8y=1210x16y=20In the following exercises, solve the systems of equations by elimination. 163. {11x+12y=6022x+24y=90In the following exercises, solve the systems of equations by elimination. 164. {7x9y=1621x+27y=24In the following exercises, solve the systems of equations by elimination. 165. {5x3y=15y= 5 3x2In the following exercises, solve the systems of equations by elimination. 166. {2x+4y=7y= 1 2x4\In the following exercises, translate to a system of equations and solve. 167. The sum of two numbers is 65. Their difference is 25. Find the numbers.In the following exercises, translate to a system of equations and solve. 168. The sum of two numbers is 37. Their difference is 9. Find the numbers.In the following exercises, translate to a system of equations and solve. 169. The sum of two numbers is 27 . Their difference is 59 . Find the numbers.In the following exercises, translate to a system of equations and solve. 170. The sum of two numbers is 45 . Their difference is 89 . Find the numbers.In the following exercises, translate to a system of equations and solve. 171. Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114 or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost?In the following exercises, translate to a system of equations and solve. 172. Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40 or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?In the following exercises, translate to a system of equations and solve. 173. The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?In the following exercises, translate to a system of equations and solve. 174. The total number of calories in 2 hot dogs and 3 cups of cottage cheese is 960 calories. The total number of calories in 5 hot dogs and 2 cups of cottage cheese is 1190 calories. How many calories are in a hot dog? How many calories are in a cup of cottage cheese?In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 175. (a) {8x15y=326x+3y=5 (b) {x=4y34x2y=6In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 176. (a) {y=7x53x2y=16 (b) {12x5y=423x+7y=15In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 177. (a) {y=4x+95x2y=21 (b) {9x4y=243x+5y=14In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 178. (a) {14x15y=307x+2y=10 (b) {x=9y112x7y=27Norris can row 3 miles upstream against the current in the same amount of time it takes him to row 5 miles downstream, with the current. Solve the system. {rc=3r+c=5 (a) for r, his rowing speed in still water. (b) Then solve for c, the speed of the river current.Josie wants to make 10 pounds of trail mix using nuts and raisins, and she wants the total cost of the trail mix to be $54. Nuts cost $6 per pound and raisins cost $3 per pound. Solve the system {n+r=106n+3r=54 to find n, the number of pounds of nuts, and r, the number of pounds of raisins she should use.Solve the system {x+y=105x+8y=56 (a)by substitution (b)by graphing (c) Which method do you prefer? Why?Solve the system {x+y=12y=4 1 2x (a) by substitution (b) by graphing (c) Which method do you prefer? Why?Translate to a system of equations: The sum of two numbers is negative twenty-three. One number is 7 less than the other. Find the numbers.Translate to a system of equations: The sum of two numbers is negative eighteen. One number is 40 more than the other. Find the numbers.Translate to a system of equations: A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns.How much does the wife earn?Translate to a system of equations: A senior employee makes $5 less than twice what a new employee makes per hour. Together they make $43 per hour. How much does each employee make per hour?Translate to a system of equations and then solve: Ali is 12 years older than his youngest sister, Jameela. The sum of their ages is 40. Find their ages.Translate to a system of equations and then solve: Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42. Find their ages.Translate to a system of equations and then solve: Mark went to the gym and did 40 minutes of Bikram hot yoga and 10 minutes of jumping jacks. He burned 510 calories. The next time he went to the gym, he did 30 minutes of Bikram hot yoga and 20 minutes of jumping jacks burning 470 calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?Translate to a system of equations and then solve: Erin spent 30 minutes on the rowing machine and 20 minutes lifting weights at the gym and burned 430 calories. During her next visit to the gym she spent 50 minutes on the rowing machine and 10 minutes lifting weights and burned 600 calories. How many calories did she burn for each minutes on the rowing machine? How many calories did she burn for each minute of weight lifting?Translate to a system of equations and then solve: The difference of two complementary angles is 20 degrees. Find the measures of the angles.Translate to a system of equations and then solve: The difference of two complementary angles is 80 degrees. Find the measures of the angles.Translate to a system of equations and then solve: Two angles are supplementary. The measure of the larger angle is 12 degrees more than three times the smaller angle. Find the measures of the angles.Translate to a system of equations and then solve: Two angles are supplementary. The measure of the larger angle is 18 less than twice the measure of the smaller angle. Find the measures of the angles.Translate to a system of equations and then solve: Mario wants to put a rectangular fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There are two long sides and the one shorter side is parallel to the house. He needs 155 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.Translate to a system of equations and then solve: Alexis wants to build a rectangular dog run in her yard adjacent to her neighbor’s fence. She will use 136 feet of fencing to completely enclose the rectangular dog run. The length of the dog run along the neighbor’s fence will be 16 feet less than twice the width. Find the length and width of the dog run.Translate to a system of equations and then solve: Mitchell left Detroit on the interstate driving south towards Orlando at a speed of 60 miles per hour. Clark left Detroit 1 hour later traveling at a speed of 75 miles per hour, following the same route as Mitchell. How long will it take Clark to catch Mitchell?Translate to a system of equations and then solve: Charlie left his mother’s house traveling at an average speed of 36 miles per hour. His sister Sally left 15 minutes (1/4 hour) later traveling the same route at an average speed of 42 miles per hour. How long before Sally catches up to Charlie?Translate to a system of equations and then solve: A Mississippi river boat cruise sailed 120 miles upstream for 12 hours and then took 10 hours to return to the dock. Find the speed of the river boat in still water and the speed of the river current.Translate to a system of equations and then solve: Jason paddled his canoe 24 miles upstream for 4 hours. It took him 3 hours to paddle back. Find the speed of the canoe in still water and the speed of the river current.Translate to a system of equations and then solve: A small jet can fly 1,325 miles in 5 hours with a tailwind but only 1035 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.Translate to a system of equations and then solve: A commercial jet can fly 1728 miles in 4 hours with a tailwind but only 1536 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.In the following exercises, translate to a system of equations. Do not solve the system. 183. The sum of two numbers is fifteen. One number is three less than the other. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 184. The sum of two numbers is twenty-five. One number is five less than the other. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 185. The sum of two numbers is negative thirty. One number is five times the other. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 186. The sum of two numbers is negative sixteen. One number is seven times the other. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 187. Twice a number plus three times a second number is twenty-two. Three times the first number plus four times the second is thirty-one. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 188. Six times a number plus twice a second number is four. Twice the first number plus four times the second number is eighteen. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 189. Three times a number plus three times a second number is fifteen. Four times the first plus twice the second number is fourteen. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 190. Twice a number plus three times a second number is negative one. The first number plus four times the second number is two. Find the numbers.In the following exercises, translate to a system of equations. Do not solve the system. 191. A married couple together earn $75,000. The husband earns $15,000 more than five times what his wife earns. What does the wife earn?In the following exercises, translate to a system of equations. Do not solve the system. 192. During two years in college, a student earned $9,500. The second year she earned $500 more than twice the amount she earned the first year. How much did she earn the first year?In the following exercises, translate to a system of equations. Do not solve the system. 193. Daniela invested a total of $50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was $5000 more than twice the amount she put into the CD. How much did she invest in each account?In the following exercises, translate to a system of equations. Do not solve the system. 194. Jorge invested $28,000 into two accounts. The amount he put in his money market account was $2,000 less than twice what he put into a CD. How much did he invest in each account?In the following exercises, translate to a system of equations. Do not solve the system. 195. In her last two years in college, Marlene received $42,000 in loans. The first year she received a loan that was $6,000 less than three times the amount of the second year’s loan. What was the amount of her loan for each year?In the following exercises, translate to a system of equations. Do not solve the system. 196. Jen and David owe $22,000 in loans for their two cars. The amount of the loan for Jen’s car is $2000 less than twice the amount of the loan for David’s car. How much is each car loan?In the following exercises, translate to a system of equations and solve. 197. Alyssa is twelve years older than her sister, Bethany. The sum of their ages is forty-four. Find their ages.In the following exercises, translate to a system of equations and solve. 198. Robert is 15 years older than his sister, Helen. The sum of their ages is sixty-three. Find their ages.In the following exercises, translate to a system of equations and solve. 199. The age of Noelle’s dad is six less than three times Noelle’s age. The sum of their ages is seventy-four. Find their ages.In the following exercises, translate to a system of equations and solve. 200. The age of Mark’s dad is 4 less than twice Marks’s age. The sum of their ages is ninety-five. Find their ages.In the following exercises, translate to a system of equations and solve. 201. Two containers of gasoline hold a total of fifty gallons. The big container can hold ten gallons less than twice the small container. How many gallons does each container hold?In the following exercises, translate to a system of equations and solve. 202. June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?In the following exercises, translate to a system of equations and solve. 203. Shelly spent 10 minutes jogging and 20 minutes cycling and burned 300 calories. The next day, Shelly swapped times, doing 20 minutes of jogging and 10 minutes of cycling and burned the same number of calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?In the following exercises, translate to a system of equations and solve. 204. Drew burned 1800 calories Friday playing one hour of basketball and canoeing for two hours. Saturday he spent two hours playing basketball and three hours canoeing and burned 3200 calories. How many calories did he burn per hour when playing basketball?In the following exercises, translate to a system of equations and solve. 205. Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought four notebooks and five thumb drives for $116. Lisa bought two notebooks and three thumb dives for $68. Find the cost of each notebook and each thumb drive.In the following exercises, translate to a system of equations and solve. 206. Nancy bought seven pounds of oranges and three pounds of bananas for $17. Her husband later bought three pounds of oranges and six pounds of bananas for $12. What was the cost per pound of the oranges and the bananas?In the following exercises, translate to a system of equations and solve. 207. The difference of two complementary angles is 30 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 208. The difference of two complementary angles is 68 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 209. The difference of two supplementary angles is 70 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 210. The difference of two supplementary angles is 24 degrees. Find the measure of the angles.In the following exercises, translate to a system of equations and solve. 211. The difference of two supplementary angles is 8 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 212. The difference of two supplementary angles is 88 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 213. The difference of two complementary angles is 55 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 214. The difference of two complementary angles is 17 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 215. Two angles are supplementary. The measure of the larger angle is four more than three times the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 216. Two angles are supplementary. The measure of the larger angle is five less than four times the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 217. Two angles are complementary. The measure of the larger angle is twelve less than twice the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 218. Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 219. Wayne is hanging a string of lights 45 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.In the following exercises, translate to a system of equations and solve. 220. Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his rectangular front yard. The length is five feet less than five times the width. Find the length and width of the fencing.In the following exercises, translate to a system of equations and solve. 221. A frame around a rectangular family portrait has a perimeter of 60 inches. The length is fifteen less than twice the width. Find the length and width of the frame.In the following exercises, translate to a system of equations and solve. 222. The perimeter of a rectangular toddler play area is 100 feet. The length is ten more than three times the width. Find the length and width of the play area.In the following exercises, translate to a system of equations and solve. 223. Sarah left Minneapolis heading east on the interstate at a speed of 60 mph. Her sister followed her on the same route, leaving two hours later and driving at a rate of 70 mph. How long will it take for Sarah’s sister to catch up to Sarah?In the following exercises, translate to a system of equations and solve. 224. College roommates John and David were driving home to the same town for the holidays. John drove 55 mph, and David, who left an hour later, drove 60 mph. How long will it take for David to catch up to John?In the following exercises, translate to a system of equations and solve. 225. At the end of spring break, Lucy left the beach and drove back towards home, driving at a rate of 40 mph. Lucy’s friend left the beach for home 30 minutes (half an hour) later, and drove 50 mph. How long did it take Lucy’s friend to catch up to Lucy?In the following exercises, translate to a system of equations and solve. 226. Felecia left her home to visit her daughter driving 45 mph. Her husband waited for the dog sitter to arrive and left home twenty minutes (1/3 hour) later. He drove 55 mph to catch up to Felecia. How long before he reaches her?In the following exercises, translate to a system of equations and solve. 227. The Jones family took a 12 mile canoe ride down the Indian River in two hours. After lunch, the return trip back up the river took three hours. Find the rate of the canoe in still water and the rate of the current.In the following exercises, translate to a system of equations and solve. 228. A motor boat travels 60 miles down a river in three hours but takes five hours to return upstream. Find the rate of the boat in still water and the rate of the current.