Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-y-z=1\\
2x+3y+z=2\\
3x+2y=0
\end{cases}$
Use the elimination method. Add the first and the second equation to eliminate $z$:
$\begin{cases}
x-y-z+2x+3y+z=1+2\\
3x+2y=0
\end{cases}$
$\begin{cases}
3x+2y=3\\
3x+2y=0
\end{cases}$
Multiply the first equation by 1 and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
-3x-2y=-3\\
3x+2y=0
\end{cases}$
$-3x-2y+3x+2y=-3+0$
$0=-3$
As we got a false statement, the system has no solution. It is inconsistent.