Answer
$x=2$
$y=-3$
$(2,-3)$
Work Step by Step
$\frac{1}{2}x+y=-2$ $(1)$
$x-2y=8$ $(2)$
Multiply Equation $(1)$ by 2
$x+2y=-4$ $(1)$
$x-2y=8$ $(2)$
Subtract Equation $(1)$ from Equation $(2)$
$2x=4$
$x=2$
Substitute back to Equation $(2)$
$2-2y = 8$
$-2y=6$
$y=-3$