find the x value that will make the equations below true by graphing the lines on a coordinate plane and determining where they intersect

Question

2x - 3y = 18
2x + y = 2

A. 1
B. 2
C. 3
D. 4

Answer 1

To find the x value where the two equations intersect, we can graph the lines of the equations on a coordinate plane.

First, let's rearrange the equations into slope-intercept form (y = mx + b):
1. 2x - 3y = 18
=> -3y = -2x + 18
=> y = (2/3)x - 6

2. 2x + y = 2
=> y = -2x + 2

Now, let's graph the two lines:

The line represented by y = (2/3)x - 6 has a y-intercept of -6 and a slope of 2/3.
The line represented by y = -2x + 2 has a y-intercept of 2 and a slope of -2.

When we plot the lines, we can see that they intersect at the point (3, -4). Therefore, the x value that makes both equations true is x = 3.

So the answer is:

C. 3