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:
$$\begin{cases}
3x-4y=4 \hspace{20pt} (1)\\[3mm]
\dfrac{1}{2}x-3y=-\dfrac{1}{2} \hspace{20pt} (2)
\end{cases}$$
Plugging in $x=2 \text{ and } y=\dfrac{1}{2} \text{ in the two equations:}$
$$\begin{cases}
3(2)-4 \left(\dfrac{1}{2} \right)=6 -2= 4 \\[3mm]
\dfrac{1}{2}(2)-3\left(\dfrac{1}{2} \right) = 1-\dfrac{3}{2}= - \dfrac{1}{2}
\end{cases}$$
$\text{Since }x=2 \text{ and } y=\dfrac{1}{2} \text{ satisfy the two equations, then}$
$x=2 \text{ and } y=\dfrac{1}{2} \text{ are solutions of the system of equations}$