Chapter 8 - Section 8.1 - Systems of Linear Equations: Substitution and Elimination - 8.1 Assess Your Understanding - Page 555: 36

$x=2$ $y=-3$ $(2,-3)$

$\frac{1}{2}x+y=-2$ $(1)$ $x-2y=8$ $(2)$ 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 $(2)$ $2-2y = 8$ $-2y=6$ $y=-3$