#### Answer

The given values of the variables are solutions of the system of equations.
$\text{See the work below.}$

#### Work Step by Step

The system of equations is given by the following three equations:
$$\begin{cases}
3x+3y+2z = 4\hspace{20pt} (1)\\[3mm]
x-3y+z= 10 \hspace{20pt} (2) \\[3mm]
5x-2y-3z=8 \hspace{20pt} (3)
\end{cases}$$
Plugging in $x=2 \text{, } y=-2 \text{ and } z=2$
$$\begin{cases}
3(2)+3(-2)+2(2)=6-6+4 = 4\\[3mm]
2-3(-2)+2 =2+6+2 = 10 \\[3mm]
5(2)-2(-2)-3(2)= 10+4-6 = 8
\end{cases}$$
$\text{Since }x=2 \text{, } y=-2 \text{ and } z=2\text{ satisfy the three equations, then}$
$x=2 \text{, } y=-2 \text{ and } z=2 \text{ are solutions of the system of equations}$