#### 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:
$$\begin{cases}
4x-z=7\hspace{20pt} (1)\\[3mm]
8x+5y-z=0 \hspace{20pt} (2) \\[3mm]
-x-y+5z=6 \hspace{20pt} (3)
\end{cases}$$
Plugging in $x=2 \text{, } y=-3 \text{ and } z=1$
$$\begin{cases}
4(2)-1 = 8-1 = 7 \\[3mm]
8(2)+5(-3)-1 = 16-15-1= 0 \\[3mm]
-2-(-3)+5(1)=-2+3+5= 6
\end{cases}$$
$\text{Since }x=2 \text{, } y=-3 \text{ and } z=1\text{ satisfy the three equations, then }$
$x=2 \text{, } y=-3 \text{ and } z=1 \text{ are solutions of the system of equations.}$