Answer
$x=-2$
$y=-1$
$z=0$
Work Step by Step
Build the augmented matrix of the system of equations;
$\begin{bmatrix}1&-2&1&|&0\\0&1&-3&|&-1\\0&2&5&|&-2\end{bmatrix}$
Bring the matrix to the row reduced echelon form:
Add $R_3$ to $R_1$:
$\begin{bmatrix}1&0&6&|&-2\\0&1&-3&|&-1\\0&2&5&|&-2\end{bmatrix}$
Add $-2R_2$ to $R_3$:
$\begin{bmatrix}1&0&6&|&-2\\0&1&-3&|&-1\\0&0&11&|&0\end{bmatrix}$
Multiply $R_3$ by $\dfrac{1}{11}$:
$\begin{bmatrix}1&0&6&|&-2\\0&1&-3&|&-1\\0&0&1&|&0\end{bmatrix}$
Add $3R_3$ to $R_2$:
$\begin{bmatrix}1&0&6&|&-2\\0&1&0&|&-1\\0&0&1&|&0\end{bmatrix}$
Add $-6R_3$ to $R_1$:
$\begin{bmatrix}1&0&0&|&-2\\0&1&0&|&-1\\0&0&1&|&0\end{bmatrix}$
The solution is:
$x=-2$
$y=-1$
$z=0$
