Answer
The system is inconsistent.
Work Step by Step
Gaussian Elimination:
$\begin{bmatrix}
-3 & 2 & |-22\\
3 & 4 & |4\\
4 & -8 & |32\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-3 & 2 & |-22\\
0 & 6 & |-18\\
1 & -2 & |8\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & -2 & |8\\
0 & 6 & |-18\\
-3 & 2 & |-22\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & -2 & |8\\
0 & 1 & |-3\\
0 & -4 & |2\\
\end{bmatrix}$
Back-Substitution:
y = -3
-4y = 2
y = $\frac{-1}{2}$
Since y has two different solutions, there is no solution to the system.
The system is inconsistent.
