Answer
No solution.
Work Step by Step
Write the augmented matrix and,
using row transformations arrive at the reduced row echelon form.
-----------
$\left[\begin{array}{lll}
1 & 2 & 1\\
3 & -2 & -2\\
5 & -1 & 1/5
\end{array}\right]\begin{array}{l}
.\\
R_{2}-3R_{1}\\
R_{3}-5R_{1}
\end{array}$, clear column $1$
$\left[\begin{array}{lll}
1 & 2 & 1\\
0 & -8 & -5\\
0 & -11 & -24/5
\end{array}\right]\begin{array}{l}
.\\
.\\
8R_{3}-11R_{2}
\end{array}$, clear column $2$
$\left[\begin{array}{lll}
1 & 2 & 1\\
0 & -8 & -5\\
0 & 0 & -184/5+55
\end{array}\right]$
No need to continue, as
the last row represents
( zero ) = (nonzero number)
so the system is inconsistent.
No solution.