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, Problem 2MCQ
To determine

To calculate: The solution set for the system of equations with the help of a graph.

  5x+2y=35x−4y=9

Expert Solution & Answer
Check Mark

Answer to Problem 2MCQ

The solution set for the system of equations is (1,−1) .

Explanation of Solution

Given information:

The system of equations

  5x+2y=35x−4y=9

Formula used:

The slope intercept of a line is y=mx+c where m is the slope and c is the intercept of y-axis.

Calculation:

Consider the system of equations

  5x+2y=35x−4y=9

Write both the equation in slope intercept form.

  5x+2y=32y=−5x+3y=−52x+32

And,

  5x−4y=94y=5x−9y=54x−94

Plot the equations y=−52x+32 and y=54x−94 on the coordinate plane.

  Algebra 2, Chapter 3, Problem 2MCQ

Red line depicts the equation 5x+2y=3 and blue line depicts the equation 5x−4y=9 .

The graph of the equations intersect at (1,−1) .

Therefore, the solution set of the system of equations is (1,−1) .

To verify substitute the point (1,−1) in the equations and check.

For the equation 5x+2y=3 , substitute x as 1 and y as −1 .

  5(1)+2(−1)=33=3

For the equation 5x−4y=9 , substitute x as 1 and y as −1 .

  5(1)−4(−1)=99=9

Both the equations satisfy the point.

Thus, the solution set for the system of equations is (1,−1) .

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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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