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

1 Answer
Oct 6, 2017

Answer:

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(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)