# How do you find the solution of the system of equations -3x+4y=12 and 3x-6y=18?

May 8, 2015

Given
$- 3 x + 4 y = 12$
$3 x - 6 y = 18$

If you add the two equations together, you get
$- 2 y = 30$
$\rightarrow y = - 15$

Plug this back into the first equation:
$- 3 x + 4 \left(- 15\right) = 12$
$- 3 x = 72$
$\rightarrow x = - 24$

It would be a good idea to check these values with the second equation:
$3 \left(- 24\right) - 6 \left(- 15\right) = - 72 + 90 = 18 \text{ and it all looks good!}$