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