Answer
The given values of the variables are solutions of the system of equations.
$\text{See the steps below.}$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
2x+\dfrac{1}{2}y=0 \hspace{20pt} (1)\\[3mm]
3x-4y=-\dfrac{19}{2} \hspace{20pt} (2)
\end{cases}$$
Plugging in $x=-\dfrac{1}{2} \text{ and } y=2 \text{ in the two equations:}$
$$\begin{cases}
2\left(-\dfrac{1}{2}\right)+\dfrac{1}{2}(2)=-1+1=0 \\[3mm]
3\left(-\dfrac{1}{2}\right)-4(2) = -\dfrac{3}{2}-8=-\dfrac{19}{2}
\end{cases}$$
$\text{Since }x=-\dfrac{1}{2} \text{ and } y=2 \text{ satisfy the two equations, then}$
$x=-\dfrac{1}{2} \text{ and } y=2 \text{ are solutions of the system of equations}$
