Answer
$(-1,.5)$
Work Step by Step
Please see the screenshot of the tables for the two equations.
Purple line: $3x+2y=-2$
Green line: $x-2y=2$
If we replace $x$ and $y$ with $0$ and $-1$, respectively, for the green line, we have
$x-2y=2$
$0-2*(-1)=2$
$0+2=2$ (true)
Purple line:
$3x+2y=-2$
$3*0+2*(-1)=-2$
$0-2=-2$ (true)
Purple line:
$3x+2y=-2$
$2y=-2-3x$
$2y/2=(-2-3x)/2$
$y=-3/2*x-1$
Green line:
$x-2y=2$
$x-2y+2y-2=2+2y-2$
$x-2=2y$
$(x-2)/2=2y/2$
$1/2*x-1=y$
Purple line: $m=-3/2$, y-intercept is -1
Green line: $m=1/2$, y-intercept is -1