Answer
Solution set: $\{(0,2,2)\}$
Work Step by Step
$\left[\begin{array}{lllll}
3 & 1 & -1 & | & 0\\
1 & 1 & 2 & | & 6\\
2 & 2 & 3 & | & 10
\end{array}\right]\left\{\begin{array}{l}
R1\leftrightarrow R2.\\
\\
.
\end{array}\right.$
$\left[\begin{array}{lllll}
1 & 1 & 2 & | & 6\\
3 & 1 & -1 & | & 0\\
2 & 2 & 3 & | & 10
\end{array}\right]\left\{\begin{array}{l}
.\\
-3R1.+R2\rightarrow R2\\
-2R1+R3\rightarrow R3.
\end{array}\right.$
$\left[\begin{array}{lllll}
1 & 1 & 2 & | & 6\\
0 & -2 & -7 & | & -18\\
0 & 0 & -1 & | & -2
\end{array}\right]\left\{\begin{array}{l}
.\\
\div(-2)\\
\times(-1).
\end{array}\right.$
$\left[\begin{array}{lllll}
1 & 1 & 2 & | & 6\\
0 & 1 & 7/2 & | & 9\\
0 & 0 & 1 & | & 2
\end{array}\right]\left\{\begin{array}{l}
.\\
.\\
\Rightarrow z=2.
\end{array}\right.$
Back substitute into row/equation 2,
$y+\displaystyle \frac{7}{2}(2)=9$
$y=9-7=2$
Back substitute into row/equation 1:
$x+(2)+2(2)=6$
$x=6-6=0$
Solution set: $\{(0,2,2)\}$
