Answer
Inconsistent (no solutions).
Work Step by Step
Start with the augmented matrix, row reduce to
reduced row echelon form (Gauss-Jordan.)
$\left[\begin{array}{rrrr}
0 & 1 & -5 & 7\\
3 & 2 & 0 & 12\\
3 & 0 & 10 & 80
\end{array}\right]\rightarrow\left(\begin{array}{l}
R_{1}\leftrightarrow R_{3}.\\
.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{rrrr}
3 & 0 & 10 & 80\\
3 & 2 & 0 & 12\\
0 & 1 & -5 & 7
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
-R_{1}.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{rrrr}
3 & 0 & 10 & 80\\
0 & 2 & -10 & -68\\
0 & 1 & -5 & 7
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
\div 2.\\
.
\end{array}\right)$
$\rightarrow\left[\begin{array}{rrrr}
3 & 0 & 10 & 80\\
0 & 1 & -5 & -34\\
0 & 1 & -5 & 7
\end{array}\right]\rightarrow\left(\begin{array}{l}
.\\
.\\
-R_{3}.
\end{array}\right)$
$\rightarrow\left[\begin{array}{rrrr}
3 & 0 & 10 & 80\\
0 & 1 & -5 & -34\\
0 & 0 & 0 & 41
\end{array}\right]$
The last row represents the equation
$0=41$
which is never true - the system has no solutions.
Inconsistent (no solutions)