Answer
No solution.
Work Step by Step
Write the augmented matrix and,
using row transformations arrive at the reduced row echelon form.
-----------
$\left[\begin{array}{lll}
1 & 1 & 0\\
3 & -1 & 1\\
1 & -1 & -1
\end{array}\right]\begin{array}{l}
.\\
R_{2}-3R_{1}\\
R_{3}-R_{1}
\end{array}$, clear column $1$
$\left[\begin{array}{lll}
1 & 1 & 0\\
0 & -4 & 1\\
0 & -2 & -1
\end{array}\right]\begin{array}{l}
.\\
.\\
R_{3}-\frac{1}{2}R_{2}.
\end{array}$, clear column $2$
$\left[\begin{array}{lll}
1 & 1 & 0\\
0 & -4 & 1\\
0 & 0 & -3/2
\end{array}\right]$
No need to continue, as
the last row represents the equation
$0=-3/2$,
so the system is inconsistent.
No solution.
