Answer
Yes, the ordered triple is a solution of the system.
Work Step by Step
We have to check if the provided point is a solution to the system, putting in the value $5$ for x, $-3$ for y and $-2$ for z in all the three equations:
For the first equation:
$\begin{align}
& 5-3-2=0 \\
& 5-5=0 \\
& 0=0
\end{align}$
This implies the point satisfies the first equation.
For the second equation:
$\begin{align}
& 5+2\left( -3 \right)-3\left( -2 \right)=5 \\
& 5-6+6=5 \\
& 5=5
\end{align}$
This implies the point satisfies the second equation.
For the third equation:
$\begin{align}
& 3x+4y+2z=-1 \\
& 3\left( 5 \right)+4\left( -3 \right)+2\left( -2 \right)=-1 \\
& 15-12-4=-1 \\
& -1=-1
\end{align}$
Thus, the ordered triple is a solution of the system.
