# How do you solve the system using the elimination method for -4x+y=-12 and 4x+2y=6?

Jul 4, 2015

First add the two equations together to get $3 y = - 6$,
hence $y = - 2$

Secondly, you can subtract twice the first equation from the second to get $12 x = 30$, hence $x = \frac{5}{2}$

#### Explanation:

Add the two equations together to get:

$- 6 = - 12 + 6 = \left(- 4 x + y\right) + \left(4 x + 2 y\right) = 3 y$

Divide both ends by $3$ to get $y = - 2$

Subtract twice the first equation from the second to get:

$30 = 6 - 2 \left(- 12\right) = \left(4 x + 2 y\right) - 2 \left(- 4 x + y\right) = 12 x$

Divide both ends by $12$ to get $x = \frac{30}{12} = \frac{5}{2}$