Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.5, Problem 41S
To determine

To calculate: The solution set of system of equations,

  5x+3y=254x+7y=−3

Expert Solution & Answer
Check Mark

Answer to Problem 41S

The solution set of the system of equations is (2,5) .

Explanation of Solution

Given information:

The system of equations is provided below,

  5x+3y=254x+7y=−3

Formula used:

A system of equations with two variables can be solved by elimination method and substitution method.

In elimination method, multiply the equations to make the constant term equal of same variable and then add or subtract them to solve.

In substitution method, substitute the value of one variable from first equation into second and simplify it further.

Calculation:

Consider the provided system of equations as,

  5x+3y=254x+7y=−3

Recall that a system of equations with two variables can be solved by elimination method and substitution method. In elimination method, multiply the equations to make the constant term equal of same variable and then add or subtract them to solve.

Apply it,

Multiply first equation by 4 and second equation by −5 and then both the equations.

  4(5x+3y)=4(25)20x+12y=100

  −5(4x+7y)=−5(−3)−20x−35y=15

Now add both the equations to eliminate x and get the value of y ,

  20x+12y=100(+)−20x−35y=15−23y=115

Simplify −23y=115 further as,

  −23y=115y=115−23y=5

Now substitute y=5 in first equation 5x+3y=25 and solve it as,

  5x+3(5)=255x+15=255x=10x=2

Thus, the solution set of the system of equations is (2,5) .

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Chapter 3.5, Problem 40S
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Chapter 3.5, Problem 42S

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
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Prob. 30HPCh. 3.5 - Prob. 31HPCh. 3.5 - Prob. 32HPCh. 3.5 - Prob. 33HPCh. 3.5 - Prob. 34STPCh. 3.5 - Prob. 35STPCh. 3.5 - Prob. 36STPCh. 3.5 - Prob. 37STPCh. 3.5 - Prob. 38STPCh. 3.5 - Prob. 39SCh. 3.5 - Prob. 40SCh. 3.5 - Prob. 41SCh. 3.5 - Prob. 42SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 7QCCh. 3 - Prob. 8QCCh. 3 - Prob. 9QCCh. 3 - Prob. 10QCCh. 3 - Prob. 11QCCh. 3 - Prob. 12QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 7MCQCh. 3 - Prob. 8MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - Prob. 13MCQCh. 3 - Prob. 14MCQCh. 3 - Prob. 15MCQCh. 3 - Prob. 16MCQCh. 3 - Prob. 17MCQCh. 3 - Prob. 18MCQCh. 3 - Prob. 19MCQCh. 3 - Prob. 20MCQCh. 3 - Prob. 21MCQCh. 3 - Prob. 22MCQCh. 3 - Prob. 1SGRCh. 3 - Prob. 2SGRCh. 3 - Prob. 3SGRCh. 3 - Prob. 4SGRCh. 3 - Prob. 5SGRCh. 3 - 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