Answer
$\left\{\left(2,-3\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
\dfrac{1}{2}x+y=-2\\
x-2y=8
\end{cases}$
Use the elimination method. Multiply the first equation by $2$ and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
2\left(\dfrac{1}{2}x+y\right)=2(-2)\\
x-2y=8
\end{cases}$
$\begin{cases}
x+2y=-4\\
x-2y=8
\end{cases}$
$x+2y+x-2y=-4+8$
$2x=4$
$x=2$
Determine $y$ using the first equation:
$\dfrac{1}{2}x+y=-2$
$\dfrac{1}{2}(2)+y=-2$
$1+y=-2$
$y=-3$
The solution set of the system is:
$\left\{\left(2,-3\right)\right\}$
