Answer
The system is inconsistent (has no solution).
Solution set =$ \emptyset.$
Work Step by Step
Method: Gauss-Jordan. Row reduce the augmented matrix:
$\left[\begin{array}{rrr|r}
{3}&{2}&{-1}&{2}\\
{2}&{1}&{6}&{-7}\\
{2}&{2}&{-14}&{17}\end{array}\right]\qquad\left\{\begin{array}{l}
R_{1}=r_{1}-r_{2}.\\
.\\
.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{1}&{-7}&{9}\\
{2}&{1}&{6}&{-7}\\
{2}&{2}&{-14}&{17}\end{array}\right] \qquad\left\{\begin{array}{l}
.\\
R_{2}=r_{2}-2r_{1}.\\
R_{3}=r_{3}-2r_{1}.
\end{array}\right\}\rightarrow$
$\rightarrow\left[\begin{array}{rrr|r}
{1}&{1}&{-7}&{9}\\
{0}&{-1}&{20}&{-25}\\
{0}&{0}&{0}&{-1}\end{array}\right]$
the last row represents the equation$ \quad 0=-1,$
which is never satisfied.
The system is inconsistent (has no solution).
Solution set =$ \emptyset.$
