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