Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 7.2, Problem 6E
To determine

To find : the solution to the given system of equation using elimination method

Expert Solution & Answer
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Answer to Problem 6E

The solution to the system of equation is (−2, 1)

Explanation of Solution

Given information : The system of equation is {   x +3y  =1−x+2y=4   

  Precalculus with Limits, Chapter 7.2, Problem 6E , additional homework tip 1

Concept Involved:

Solution of a system of equation is the point which makes both the equation TRUE.

Graphically the solution to the system of equation is the point where the two lines meet.

Method of Elimination: To use the method of elimination to solve a system of two linear equations in x and y  , perform the following steps:

1. Obtain coefficients for x (or y) that differ only in sign by multiplying allterms of one or both equations by suitably chosen constants.

2. Add the equations to eliminate one variable.

3. Solve the equation obtained in Step 2.

4. Back-substitute the value obtained in Step 3 into either of the originalequations and solve for the other variable.

5. Check that the solution satisfies each of the original equations.

Calculation:

    DescriptionSteps
    Label the given system of equation   x +3y  =1    →1stEquation
    −x+2y=4   →2ndEquation
    Add 1st and 2nd equation to eliminate the ‘x’ variable   x +3y  =1−x+2y=4_            5y=5
    Divide 5 on both sides of the equation 5y=55y5=55
    Simplify fraction on both sides of the equationy=1
    Substitute 1 for y in the 1st equationx+3(1)=1
    Simplify in left side of the equationx+3=1
    Subtract 3 on both sidesx+3−3=1−3
    Combine like terms in left side of the equationx=−2

Conclusion:

The solution to the given system of equation is (−2, 1) and it matches with the given graph.

  Precalculus with Limits, Chapter 7.2, Problem 6E , additional homework tip 2

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Chapter 7.2, Problem 5E
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Chapter 7.2, Problem 7E

Chapter 7 Solutions

Precalculus with Limits

Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
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