Answer
Inconsistent (no solution).
Work Step by Step
Start with the augmented matrix, row reduce to
reduced row echelon form (Gauss-Jordan.)
$\left[\begin{array}{rrrr}
1 & 1 & 1 & 2\\
0 & 1 & -3 & 1\\
2 & 1 & 5 & 0
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
.\\
-2R_{1}
\end{array}\right)$
$\rightarrow\left[\begin{array}{rrrr}
1 & 1 & 1 & 2\\
0 & 1 & -3 & 1\\
0 & -1 & 3 & -3
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
.\\
+R_{2}
\end{array}\right)$
$\rightarrow\left[\begin{array}{rrrr}
1 & 1 & 1 & 2\\
0 & 1 & -3 & 1\\
0 & 0 & 0 & -2
\end{array}\right]$
The last row represents the equation
$0=2,$
which is never true - there are no solutions to the system.