Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Chapter 10.2, Problem 36E
To determine

To calculate:The solution of linear equation

Expert Solution & Answer
Check Mark

Answer to Problem 36E

  x=−1 , y=1 , z=−1 , w=1

The equation is linear.

Explanation of Solution

Given information:

  x+y+z+w=0x+y+2z+2w=02x+2y+3z+4w=12x+3y+4z+5w=2

Calculation:

Naming the given equations as,

  x+y+z+w=0.........(1)x+y+2z+2w=0.........(2)2x+2y+3z+4w=1.........(3)2x+3y+4z+5w=2.........(4)

Eliminate x from equation (2) ,

Multiplying equation (1) by −1 ,

  (x+y+z+w=0)×(−1)(x+y+z+w)×(−1)=0×(−1)(x×(−1))+(y×(−1))+(z×(−1))+(w×(−1))=0−x+(−y)+(−z)+(−w)=0−x−y−z−w=0

Naming it as equation (5) ,

  −x−y−z−w=0.........(5)

Adding equation (2) and equation (5) ,

  (x+y+2z+2w=0)+(−x−y−z−w=0)(x+y+2z+2w)+(−x−y−z−w)=0+0(x−x)+(y−y)+(2z−z)+(2w−w)=00+0+1z+1w=0z+w=0

Naming it as equation (6) ,

  z+w=0........(6)

Eliminate x from equation (3) ,

Multiplying equation (1) by −2 ,

  (x+y+z+w=0)×(−2)(x×(−2))+(y×(−2))+(z×(−2))+(w×(−2))=0×(−2)−2x+(−2y)+(−2z)+(−2w)=0−2x−2y−2z−2w=0

Naming it as equation (7) ,

  −2x−2y−2z−2w=0........(7)

Adding equation (3) and equation (7) ,

  (2x+2y+3z+4w=1)+(−2x−2y−2z−2w=0)(2x−2x)+(2y−2y)+(3z−2z)+(4w−2w)=1+00+0+1z+2w=11z+2w=1z+2w=1

Naming it as equation (8) ,

  z+2w=1........(8)

Eliminate x from equation (4) ,

Adding equation (4) and equation (7) ,

  (2x+3y+4z+5w=2)+(−2x−2y−2z−2w=0)(2x−2x)+(3y−2y)+(4z−2z)+(5w−2w)=2+00+1y+2z+3w=2y+2z+3w=2

Naming it as equation (9) ,

  y+2z+3w=2........(9)

Eliminate z from equation (4) ,

Multiplying equation (8) by −1 ,

  (z+2w=1)×(−1)(z×(−1))+(2w×(−1))=1×(−1)−z+(−2w)=−1−z−2w=−1

Naming it as equation (10) ,

  −z−2w=−1........(10)

Adding equation (6) and equation (10) ,

  (z+w=0)+(−z−2w=−1)(z−z)+(w−2w)=0+(−1)0+(−1w)=0−1−1w=−1w=−1−1w=1

By back substitution,

Solving for z ,

Put w=1 in equation (8) ,

  z+2w=1z+(2×1)=1z+2=1z=1−2z=−1

Solving for y ,

Substitute z=−1 and w=1 in equation (9) ,

  y+2z+3w=2y+(2×(−1))+(3×1)=2y+(−2)+3=2y+(−2+3)=2y+1=2y=2−1y=1

Solving for x ,

Substitute z=−1 , w=1 and y=1 in equation (1) ,

  x+y+z+w=0x+1+(−1)+1=0x+1−1+1=0x+1=0x=0−1x=−1

Therefore, the final solution is (x,y,z,w)=(−1,1,−1,1)

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Chapter 10.2, Problem 35E
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Chapter 10.2, Problem 37E

Chapter 10 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 10.1 - The system of equations {2x+3y=75xy=9 is a system...Ch. 10.1 - Prob. 2ECh. 10.1 - A system of two linear equations in two variables...Ch. 10.1 - The following is a system of two linear equations...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Prob. 55ECh. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Value of Coins A man has 14 coins in his pocket,...Ch. 10.1 - Admission Fees The admission fee at an amusement...Ch. 10.1 - Gas Station A gas station sells regular gas for...Ch. 10.1 - Fruit Stand A fruit stand sells two varieties of...Ch. 10.1 - Airplane Speed A man flies a small airplane from...Ch. 10.1 - Boat Speed A boat on a river travels downstream...Ch. 10.1 - Nutrition A researcher performs an experiment to...Ch. 10.1 - Coffee Blends A customer in a coffee shop...Ch. 10.1 - Mixture Problem A chemist has two large containers...Ch. 10.1 - Mixture Problem A biologist has two brine...Ch. 10.1 - Investments A woman invests a total of 20,000 in...Ch. 10.1 - Investments A man invests his savings in two...Ch. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Area of a Triangle Find the area of the triangle...Ch. 10.1 - Prob. 75ECh. 10.2 - These exercises refer to the following system:...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - 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Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RECh. 10 - Prob. 72RECh. 10 - Prob. 73RECh. 10 - Prob. 74RECh. 10 - Prob. 75RECh. 10 - Prob. 76RECh. 10 - Prob. 77RECh. 10 - Prob. 78RECh. 10 - Prob. 79RECh. 10 - Prob. 80RECh. 10 - Prob. 81RECh. 10 - Prob. 82RECh. 10 - Prob. 83RECh. 10 - Prob. 84RECh. 10 - Prob. 85RECh. 10 - Prob. 86RECh. 10 - Prob. 87RECh. 10 - Prob. 88RECh. 10 - Prob. 89RECh. 10 - Prob. 90RECh. 10 - Prob. 91RECh. 10 - Prob. 92RECh. 10 - Prob. 93RECh. 10 - Prob. 94RECh. 10 - Prob. 95RECh. 10 - Prob. 96RECh. 10 - Prob. 97RECh. 10 - Prob. 98RECh. 10 - Prob. 99RECh. 10 - Prob. 100RECh. 10 - Prob. 101RECh. 10 - Prob. 102RECh. 10 - Prob. 103RECh. 10 - Prob. 104RECh. 10 - Prob. 105RECh. 10 - Prob. 106RECh. 10 - Prob. 107RECh. 10 - Prob. 108RECh. 10 - Prob. 109RECh. 10 - Prob. 110RECh. 10 - Prob. 111RECh. 10 - Prob. 112RECh. 10 - Prob. 1TCh. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - Prob. 6TCh. 10 - Prob. 7TCh. 10 - Anne, Barry, and Cathy enter a coffee shop. Anne...Ch. 10 - Prob. 9TCh. 10 - Prob. 10TCh. 10 - Only one of the following matrices has an inverse....Ch. 10 - Prob. 12TCh. 10 - Prob. 13TCh. 10 - Prob. 14TCh. 10 - Find the maximum and minimum values of the given...Ch. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Find the maximum and minimum value of the given...Ch. 10 - Making Furniture A furniture manufacturer makes...Ch. 10 - A Housing Development A housing contractor has...Ch. 10 - Hauling Fruit A trucker hauls citrus fruit from...Ch. 10 - Manufacturing Calculators A manufacturer of...Ch. 10 - Shipping Televisions An electronics discount chain...Ch. 10 - Prob. 10PCh. 10 - Packaging Nuts A confectioner sells two types of...Ch. 10 - Feeding Lab Rabbits A biologist wishes to feed...Ch. 10 - Investing in Bonds A woman wishes to invest 12,000...Ch. 10 - Prob. 14PCh. 10 - Business Strategy A small software company...Ch. 10 - Feasible Region All parts of this problem refer to...
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