Answer
x = 4
y = -3
z = 2
Work Step by Step
NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form.
$\begin{bmatrix}
1 & 0 & -3 & |-2\\
3 & 1 & -2 & |5\\
2 & 2 & 1 & |4\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & -3 & |-2\\
0 & 1 & 7 & |11\\
0 & 2 & 7 & |8\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & -3 & |-2\\
0 & 1 & 7 & |11\\
0 & 0 & -7 & |-14\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & -3 & |-2\\
0 & 1 & 7 & |11\\
0 & 0 & 1 & |2\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & 0 & |4\\
0 & 1 & 0 & |-3\\
0 & 0 & 1 & |2\\
\end{bmatrix}$
From reduced row-echelon form the solution is simple:
x = 4
y = -3
z = 2
