Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x-3y-z=0\\
-x+2y+z=5\\
3x-4y-z=1
\end{cases}$
Use the elimination method. Add the second equation to the first, and then add it to the third equation:
$\begin{cases}
2x-3y-z-x+2y+z=0+5\\
3x-4y-z-x+2y+z=1+5
\end{cases}$
$\begin{cases}
x-y=5\\
2x-2y=6
\end{cases}$
$\begin{cases}
x-y=5\\
x-y=3
\end{cases}$
Multiply the first equation by -1, and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
-x+y=-5\\
x-y=3
\end{cases}$
$-x+y+x-y=-5+3$
$0=-2$
As we got a false statement, the system has no solution; it is inconsistent.
