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

Oct 6, 2017

(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 $\frac{2}{1}$).

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

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

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

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