Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 7.1, Problem 12E
To determine

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

Expert Solution & Answer
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Answer to Problem 12E

The solutions to the given system of equation are (−2,2) , (0,0) & (2,−2)

Explanation of Solution

Given information : The system of equation is {x+y=0x3−5x−y=0   

  Precalculus with Limits, Chapter 7.1, Problem 12E , 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 Substitution:

1. Solve one of the equations for one variable in terms of the other.

2. Substitute the expression found in Step 1 into the other equation to obtain an equation in one variable.

3. Solve the equation obtained in Step 2.

4. Back-substitute the value obtained in Step 3 into the expression obtained in Step 1 to find the value of the other variable.

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

Calculation:

    DescriptionSteps
    Label the given equationx+y=0       →1stEquationx3−5x−y=0   →2ndEquation
    Solve the 1stequation for variable y Subtract x on both sides of the equation x+y=0x+y−x=0−xy=−x
    Substitute −x for y in the 2nd equationx3−5x−(−x)=0
    Negative of negative is positivex3−5x+x=0
    Combine like terms in left side of the equationx3−4x=0
    Factor x in the left side of the equationx(x2−4)=0
    Use the zero factor property to set each factor to zerox=0x2−4=0
    Solve the equation x2−4=0
    Add 4 on both sides
    Simplify the equation Taking square root on both sides    		x2−4+4=0+4x2=4x2=4x=±2
    Substitute −2  for x  in the equation y=−xy=−(−2)     =2
    Substitute 0 for x  in the equation y=−xy=−(0)     =0
    Substitute 2 for x  in the equation y=−xy=−2

Conclusion:

The solutions to the given system of equation are (−2,2) , (0,0) & (2,−2) and it matches with the given graph.

  Precalculus with Limits, Chapter 7.1, Problem 12E , additional homework tip 2

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Chapter 7.1, Problem 11E
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Chapter 7.1, Problem 13E

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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