Answer
$$x_1=-2,\quad x_2= 0, \quad x_3=1.$$
Work Step by Step
We have the system
$$\left[ \begin {array}{ccc} 1&1&2\\ 1&-1&1
\\ 0&-1&2\end {array} \right]
\left[\begin{array}{rrr}{x_1}\\ {x_2} \\{x_3} \end{array}\right]=\left[\begin{array}{rrr}{0} \\ {-1}\\{2} \end{array}\right].$$
The coefficients matrix $A= \left[ \begin {array}{ccc} 1&1&2\\ 1&-1&1
\\ 0&-1&2\end {array} \right]
$ has the inverse
$$A^{-1}= \left[ \begin {array}{ccc} \frac{1}{5}&\frac{4}{5}&-\frac{3}{5}\\ \frac{2}{5}&-\frac{2}{5}&
-\frac{1}{5}\\ \frac{1}{5}&-\frac{1}{5}&\frac{2}{5}\end {array} \right]
.
$$
The system has the solution
$$\left[\begin{array}{rrr}{x_1}\\ {x_2} \\{x_3} \end{array}\right]=\left[ \begin {array}{ccc} \frac{1}{5}&\frac{4}{5}&-\frac{3}{5}\\ \frac{2}{5}&-\frac{2}{5}&
-\frac{1}{5}\\ \frac{1}{5}&-\frac{1}{5}&\frac{2}{5}\end {array} \right]\left[\begin{array}{rrr}{0} \\ {-1}\\{2} \end{array}\right]=\left[ \begin {array}{c} -2\\ 0\\ 1\end {array} \right]
.$$
That is
$$x_1=-2,\quad x_2= 0, \quad x_3=1.$$
