#### Answer

Yes, the ordered triple is a solution of the system.

#### Work Step by Step

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