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