Answer
$x=-3$
$y=\dfrac{1}{2}$
$z=1$
Work Step by Step
Build the augmented matrix of the system of equations;
$\begin{bmatrix}1&2&-1&|&-3\\2&-4&1&|&-7\\-2&2&-3&|&4\end{bmatrix}$
Use Gauss-Jordan elimination:
Add $R_3$ to $R_2$:
$\begin{bmatrix}1&2&-1&|&-3\\0&-2&-2&|&-3\\-2&2&-3&|&4\end{bmatrix}$
Add $2R_1$ to $R_3$:
$\begin{bmatrix}1&2&-1&|&-3\\0&-2&-2&|&-3\\0&6&-5&|&-2\end{bmatrix}$
Add $R_2$ to $R_1$ and $3R_2$ to $R_3$:
$\begin{bmatrix}1&0&-3&|&-6\\0&-2&-2&|&-3\\0&0&-11&|&-11\end{bmatrix}$
Multiply $R_2$ by $-\dfrac{1}{2}$ and $R_3$ by $-\dfrac{1}{11}$:
$\begin{bmatrix}1&0&-3&|&-6\\0&1&1&|&\dfrac{3}{2}\\0&0&1&|&1\end{bmatrix}$
Add $3R_3$ to $R_1$ and $-R_3$ to $R_2$:
$\begin{bmatrix}1&0&0&|&-3\\0&1&0&|&\dfrac{1}{2}\\0&0&1&|&1\end{bmatrix}$
The solution is:
$x=-3$
$y=\dfrac{1}{2}$
$z=1$
