Answer
x = -1
y = -4
Work Step by Step
NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form.
$\begin{bmatrix}
-2 & 6 & |-22\\
1 & 2 & |-9\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 3 & |-11\\
1 & 2 & |-9\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 3 & |-11\\
0 & 5 & |-20\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 3 & |-11\\
0 & 1 & |-4\\
\end{bmatrix}$ ~ $\begin{bmatrix}
-1 & 0 & |1\\
0 & 1 & |-4\\
\end{bmatrix}$ ~ $\begin{bmatrix}
1 & 0 & |-1\\
0 & 1 & |-4\\
\end{bmatrix}$
From reduced row-echelon form the solution is simple:
x = -1
y = -4
