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