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Chapter 5: Q. 30 (page 595)

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

2x-y=42x+3y=12

Short Answer

Expert verified

The solutions to the system of equations arex=3andy=2.

Step by step solution

01

Step 1. Given information.

We have:

2x-y=42x+3y=12

02

Step 2. Find the intercepts.   

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

The system of equations are:

2x-y=42x+3y=12

x-intercept: substitute y=0

2x-0=4x=2

X-intercept: 2,0

2x+3(0)=12x=6

X-intercept: 6,0

y-intercept: substitute x=0

2(0)-y=4y=-4

Y-intercept: 0,-4

2(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 3,2.

Therefore, the solutions are:

x=3,y=2

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