EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Chapter 7.1, Problem 11E
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 11E

The solutions to the given system of equation are (0,0) & (2,−4)

Explanation of Solution

Given information : The system of equation is {x2+y=0x2−4x−y=0   

  EBK PRECALCULUS W/LIMITS, Chapter 7.1, Problem 11E , 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 equationx2+y=0       →1stEquationx2−4x−y=0   →2ndEquation
    Solve the 1stequation for variable y Subtract x2 on both sides of the equation x2+y=0x2+y−x2=0−x2y=−x2
    Substitute −x2 for y in the 2nd equationx2−4x−(−x2)=0
    Negative of negative is positivex2−4x+x2=0
    Combine like terms in left side of the equation2x2−4x=0
    Factor 2x in the left side of the equation2x(x−2)=0
    Use the zero factor property to set each factor to zero2x=0x−2=0
    Solve the equation 2x=0
    Divide 2 on both sides
    Simplify fraction on both sides     		2x2=02 x=0
    Solve the equation x−2=0
    Add 2 on both sides
    Simplify the equation    		x−2+2=0+2x=2
    Substitute 0 for x in the equation y=−x2y=−02     =0
    Substitute 2 for x  in the equation y=−x2y=−22     =−4

Conclusion:

The solutions to the given system of equation are (0,0) & (2,−4) and it matches with the given graph.

  EBK PRECALCULUS W/LIMITS, Chapter 7.1, Problem 11E , additional homework tip 2

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Chapter 7.1, Problem 10E
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Chapter 7.1, Problem 12E

Chapter 7 Solutions

EBK PRECALCULUS W/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
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - 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Prob. 17PS
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