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Chapter 5: Q. 29 (page 595)

In the following exercises, solve the following systems of equations by graphing.

-2x+3y=3x+3y=12

Short Answer

Expert verified

The solutions to the system of equations arex=3andy=3.

Step by step solution

01

Step 1. Given information.

We have:

-2x+3y=3x+3y=12

02

Step 2. Find the intercepts.    

We will find thex-intercept andy-intercept of both equations and use them to graph the lines.

The system of equations are:

-2x+3y=3x+3y=12

x-intercept: substitute y=0

-2x+3(0)=3x=-1.5

X-intercept: -1.5,0

x+3(0)=12x=12

X-intercept: 12,0

y-intercept: substitute x=0

-2(0)+3y=3y=1

Y-intercept: 0,1

0+3y=12y=4

Y-intercept:0,4

03

Step 3. Use the intercept to draw the graph. 

Graph the line and find the intersection point:

The lines intersect at 3,3.

Therefore, the solutions are:

x=3,y=3

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