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 11SGR
To determine

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

  3x+4y=8x3y=6

Expert Solution & Answer
Check Mark

Answer to Problem 11SGR

The solution set for the system of equations is (0,2) .

Explanation of Solution

Given information:

The system of equations

  3x+4y=8x3y=6

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

  3x+4y=8x3y=6

Take the first equation 3x+4y=8 and write it in slope intercept form.

Subtract both sides by 3x ,

  4y=83x

Divide both sides by 4,

  y=83x4y=843x4y=34x+2

Take the second equation x3y=6 and write it in slope intercept form.

Subtract both sides by x ,

  3y=6x3y=6+x

Divide both sides by 3,

  3y=6xy=6+x3y=63+x3y=13x+2

Plot the equations y=34x+2 and y=13x+2 on the coordinate plane.

  Algebra 2, Chapter 3, Problem 11SGR

Red line depicts the equation y=34x+2 and blue line depicts the equation y=13x+2 .

The graph of the equations intersect at (0,2) .

Therefore, the solution set of the system of equations is (0,2) .

To verify substitute the point (0,2) in the equations and check.

For the equation 3x+4y=8 , substitute x as 0 and y as 2.

  3(0)+4(2)=88=8

For the equation x3y=6 , substitute x as 0 and y as 2.

  03(2)=66=6

Both the equations satisfy the point.

Thus, the solution set for the system of equations is (0,2) .

Chapter 3 Solutions

Algebra 2

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