Question

How do you solve the system `5x+2y=-15` and `y=2x-12` by graphing?

Answer 1

(1, -10)

Explanation:

You can use desmos.com to graph these for free and then you just click on the point of intersection, but if you had to do it by hand...

Blue line:
y = 2x - 12 can be graphed by starting at -12 on the y-axis (because the y-intercept is -12) and going up 2 and over 1 for every point going forward (because the slope is `2/1`).

Red line:
`5x+2y=-15` can be graphed quickly by finding x and y intercepts.

Plug in 0 for x and you can find the y-intercept:
`5(0)+2y=-15`
`2y=-15`
`y=-7.5`

Plug in 0 for y and you can find the x-intercept:
`5x+2(0)=-15`
`5x=-15`
`x=-3`

Then you just connect a line between those points and see where they cross. In this case it is (1,-10)