Answer
Inconsistent (no solution).
Work Step by Step
Start with the augmented matrix, row reduce to
reduced row echelon form (Gauss-Jordan.)
$\left[\begin{array}{llll}
1 & -1 & 3 & 3\\
4 & -8 & 32 & 24\\
2 & -3 & 11 & 4
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
-4R_{1}.\\
-2R_{1}.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & -1 & 3 & 3\\
0 & -4 & 20 & 12\\
0 & -1 & 5 & -2
\end{array}\right]\rightarrow\left(\begin{array}{l}
+R_{3}.\\
\div(-4).\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 0 & 8 & 1\\
0 & 1 & -5 & -3\\
0 & -1 & 5 & -2
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
.\\
+R_{2}.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 0 & 8 & 1\\
0 & 1 & -5 & -3\\
0 & 0 & 0 & -5
\end{array}\right]$
The last row represents the equation
$0=-5,$
which is never true - there are no solutions to the system.
Inconsistent (no solution).