# How do you solve the following system: 2x-5y=-19, 3x+2y =0 ?

Dec 9, 2015

$x = - 2 , y = 3$

#### Explanation:

$2 x - 5 y = - 19 , 3 x + 2 y = 0$

$3 x + 2 y = 0$
$3 x = - 2 y + 0$
$x = - \frac{2}{3} y$

Plug in $x$ for $2 x - 5 y = - 19$

$2 \left(- \frac{2}{3} y\right) - 5 y = - 19$
$- \frac{4}{3} y - 5 y = - 19$
$- \frac{4}{3} y - \frac{15}{3} y = - 19$
$- \frac{19}{3} y = - 19$
$3 \left(- \frac{19}{3} y\right) = 3 \left(- 19\right)$
$- 19 y = - 57$
$y = 3$

Plug in $y$ in $x = - \frac{2}{3} y$ to get $x$

$x = - \frac{2}{3} \left(3\right)$
$x = - 2$

$x = - 2 , y = 3$