# How do you solve the following system?:  x + 2y = 6 , 3x + 4 = -4y

Apr 7, 2018

x = -16, y = 11

#### Explanation:

I’m going to be using elimination:

First isolate 4 by subtracting 3x from both sides:

$3 x + 4 = - 4 y$
$- 3 x - 4 y = 4$

Now I’m going to line the two equations up to see which variable I can cancel out first

$x + 2 y = 6$
$- 3 x - 4 y = 4$

I choose $y$ because it seems to be the cleanest out of the two. Now multiply the first equation by 2 in order to cancel out $y$ and then solve for $x$

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

$2 x + 4 y = 12$
$+$
$- 3 x - 4 y = 4$
———————
$- x = 16$
$x = - 16$

Time to solve for $y$ by plugging in $- 16$ for $x$ in either equation. It’s best to choose the equation that seems more efficient

$\left(- 16\right) + 2 y = 6$
$+ 16$

$\frac{2 y}{2} = \frac{22}{2}$

$y = 11$