# How do you solve the following system: 3x + 4y = -2, 3x + 2y = 1?

Jan 3, 2016

I found:
$x = \frac{4}{3}$
$y = - \frac{3}{2}$

#### Explanation:

We can try multiplying the first equation by $- 1$ and add (in columns) to the second:
$\left\{\begin{matrix}\left(- 1\right) 3 x + 4 y = - 2 \\ 3 x + 2 y = 1\end{matrix}\right.$
$\left\{\begin{matrix}- 3 x - 4 y = 2 \\ 3 x + 2 y = 1\end{matrix}\right.$ add them:
$0 - 2 y = 3$
$y = - \frac{3}{2}$
Substitute this value into the first equation:
$3 x + 4 \left(- \frac{3}{2}\right) = - 2$
$3 x - 6 = - 2$
$x = \frac{4}{3}$