Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x-2y+3z=6\\
4x-3y+2z=0\\
-2x+3y-7z=1
\end{cases}$
Use the elimination method. Add the third equation to the first. Then multiply the third equation by 2 and add it to the second equation, to eliminate $x$:
$\begin{cases}
2x-2y+3z-2x+3y-7z=6+1\\
4x-3y+2z+2(-2x+3y-7z)=0+2(1)
\end{cases}$
$\begin{cases}
y-4z=7\\
3y-12z=2
\end{cases}$
$\begin{cases}
y-4z=7\\
y-4z=\dfrac{2}{3}
\end{cases}$
Multiply the first equation by -1 and add it to the second equation to eliminate $y$ and determine $z$:
$\begin{cases}
-y+4z=-7\\
y-4z=\dfrac{2}{3}
\end{cases}$
$-y+4z+y-4z=-7+\dfrac{2}{3}$
$0=-\dfrac{19}{3}$
As we got a false statement, the system has no solution. Therefore it is inconsistent.