Answer
The system is inconsistent (has no solutions)
Work Step by Step
Start with the augmented matrix, row reduce to
reduced row echelon form (Gauss-Jordan.)
$\left[\begin{array}{llll}
2 & 1 & 3 & 9\\
-1 & 0 & -7 & 10\\
3 & 2 & -1 & 4
\end{array}\right]\rightarrow\left(\begin{array}{l}
+R_{2}.\\
.\\
+3R_{2}.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 1 & -4 & 19\\
-1 & 0 & -7 & 10\\
0 & 2 & -22 & 44
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
+R_{1}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 1 & -4 & 19\\
0 & 1 & -11 & 29\\
0 & 2 & -22 & 44
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
.\\
-2R_{2}.
\end{array}\right)$
$\rightarrow\left[\begin{array}{llll}
1 & 1 & -4 & 19\\
0 & 1 & -11 & 29\\
0 & 0 & 0 & -14
\end{array}\right]$
The last row represents the equation
$0=-14$
which is never true - the system is inconsistent (has no solutions)