# How do you solve the system of equations: y=3x -10 and x= 12- 4y?

Mar 30, 2015

Re-write the equations in the form
$a y + b x = c$
then solve as normal.

$y = 3 x - 10$ becomes
$y - 3 x = - 10$ (equation 1)

$x = 12 - 4 y$ becomes
$4 y + x = 12$ (equation 2)

Multiply equation 1 by 4, giving
$4 y - 12 x = - 40$ and subtract from equation 2

$13 x = 52$
$\rightarrow x = 4$

Substituting back in any of the earlier equations gives
$y = 2$