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:
$$\begin{cases}
4x-5z=6\hspace{20pt} (1)\\[3mm]
5y-z=-17 \hspace{20pt} (2) \\[3mm]
-x-6y+5z=24 \hspace{20pt} (3)
\end{cases}$$
Plugging in $x=4 \text{, } y=-3 \text{ and } z=2$
$$\begin{cases}
4(4)-5(2) = 16-10 = 6\\[3mm]
5(-3)-2 = -15-2 = -17\\[3mm]
-4-6(-3)+5(2) = -4+18+10 =24
\end{cases}$$
$\text{Since }x=4 \text{, } y=-3 \text{ and } z=2\text{ satisfy the three equations, then}$
$x=4 \text{, } y=-3 \text{ and } z=2\text{ are solutions of the system of equations.}$
