# How do you solve 5x - 3y = 16 and 4x + 5y = -2?

Aug 12, 2015

I found:
$x = 2$
$y = - 2$

#### Explanation:

I would multiply the first equation by $- 4$ and the second by $5$ and then add them together (in columns):
$\left\{\begin{matrix}\left(- 4\right) \left[5 x - 3 y = 16\right] \\ \left(5\right) \left[4 x + 5 y = - 2\right]\end{matrix}\right.$

$\left\{\begin{matrix}- 20 x + 12 y = - 64 \\ 20 x + 25 y = - 10\end{matrix}\right.$ add them:
$0 + 37 y = - 74$
$y = - \frac{74}{37}$
$y = - 2$
Substitute this back into the first equation:
$5 x + 6 = 16$
$x = \frac{10}{5} = 2$