Answer
$\{(-5,2)\}$
Work Step by Step
Use Gauss-Jordan to perform the row operations given, we have:
$\begin{bmatrix} 3 & 5 & -5 \\ -2 & 3 & 16 \end{bmatrix} \begin{array} .\\3R2+2R1\to R2\\ \end{array}$
$\begin{bmatrix} 3 & 5 & -5 \\ 0 & 19 & 38 \end{bmatrix} \begin{array} .\\R2/19\to R2\\ \end{array}$
$\begin{bmatrix} 3 & 5 & -5 \\ 0 & 1 & 2 \end{bmatrix} \begin{array} .R1-5R2\to R1\\ \\ \end{array}$
$\begin{bmatrix} 3 & 0 & -15 \\ 0 & 1 & 2 \end{bmatrix} \begin{array} .R1/3\to R1\\ \\ \end{array}$
$\begin{bmatrix} 1 & 0 & -5 \\ 0 & 1 & 2 \end{bmatrix} \begin{array} . \\ \\ \end{array}$
Thus the solution set is $\{(-5,2)\}$
