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 14E
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 14E

The solutions to the given system of equation are (−3,−4) & (5,0)

Explanation of Solution

Given information : The system of equation is {−12x+y=−52x2+y2=25   

  EBK PRECALCULUS W/LIMITS, Chapter 7.1, Problem 14E , 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 equation−12x+y=−52      →1stEquationx2+y2=25           →2ndEquation
    Add 12x on both sides of the equation −12x+y+12x=12x−52 
    Simplify the left side of the equationy=12x−52
    Substitute 12x−52 for y in the 2nd equation x2+(12x−52)2=25
    Expand (12x−52)2x2+14x2+2⋅(12x)⋅(−52)+(−52)2=25
    Simplify the left side of the equationx2+14x2−52x+254=25
    Multiply 4 through the equation4x2+4⋅14x2−4⋅52x+4⋅254=4⋅25
    Simplify the left side of the equation4x2+x2−10x+25=100
    Get all the terms in one side of the equation5x2−10x+25−100=100−100
    Simplify the equation5x2−10x−75=0
    Divide by 5 throughout the equation5x2/5−10x/5−75/5=0/5
    Simplify the fraction throughout the equationx2−2x−15=0
    Factor the left side of the equation(x−5)(x+3)=0
    Use the zero factor property to set each factor to zerox+3=0x−5=0
    Solve the equation x+3=0 Subtract3 on both sides Simplify the equationx+3−3=0−3x=−3
    Solve the equation x−5=0 Add 5 on both sides Simplify the equationx−5+5=0+5x=5
    Substitute −3 for x  in the equation y=12x−52y=12(−3)−52     =−4
    Substitute 5  for x  in the equation y=12x−52y=12(5)−52     =0

Conclusion:

The solutions to the given system of equation are (−3,−4) & (5,0) and it matches with the given graph.

  EBK PRECALCULUS W/LIMITS, Chapter 7.1, Problem 14E , additional homework tip 2

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Chapter 7.1, Problem 13E
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Chapter 7.1, Problem 15E

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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