#### Answer

The solution is
$x=1 $ and $y=-2 $

#### Work Step by Step

The equations are
$3x+4y=-5 $ ... (1)
$2x-3y=8 $ ... (2)
Multiply equation (1)by $-2$ and equation (2) by $3$.
$ -6x-8y=10 $
$6x-9y=24 $
Add both equations.
$ -17y=34 $
$y=\frac{34}{-17}$
$ y=-2 $ Substitute into equation (1).
$ 3x+4(-2)=-5 $
$ 3x-8=-5 $
$ 3x=-5+8 $
$3x=3 $
$ x=1 $.