Answer
$$x_1=2, \quad x_2=-2, \quad x_3=3, \quad x_4=-5, \quad x_5=1.$$
Work Step by Step
The augmented matrix is given by
$$\left[ \begin {array}{cccccc} 1&-1&2&2&6&6\\ 3&-2&4
&4&12&14\\ 0&1&-1&-1&-3&-3\\ 2&-2&
4&5&15&10\\ 2&-2&4&4&13&13\end {array} \right]
.
$$
Using Maple program, we get
$$ \left[ \begin {array}{cccccc} 1&-1&2&2&6&6\\ 0&1&-2
&-2&-6&-4\\ 0&0&1&1&3&1\\ 0&0&0&1&
3&-2\\ 0&0&0&0&1&1\end {array} \right]
.
$$
Now, the crossposting system is given by
$$
\begin{align*}
x_1-x_2+2x_3+2x_4+6x_5&=6 \\
x_2-2x_3-2x_4-6x_5&=-4\\
x_3+x_4+3x_5&=1\\
x_4+3x_5&=-2\\
x_5&=1.
\end{align*}
$$
The above system has the solution
$$x_1=2, \quad x_2=-2, \quad x_3=3, \quad x_4=-5, \quad x_5=1.$$
