Answer
Inconsistent system, no solution.
Work Step by Step
Write the augmented matrix and,
using row transformations,
arrive at the row-reduced echelon form.
$\left[\begin{array}{llll}
0 & 1 & -5 & 7\\
3 & 2 & 0 & 12\\
3 & 0 & 10 & 80
\end{array}\right]\ \ \begin{array}{l}
R_{1}\leftrightarrow R_{2}.\\
.\\
.
\end{array}$
$\left[\begin{array}{llll}
3 & 2 & 0 & 12\\
0 & 1 & -5 & 7\\
3 & 0 & 10 & 80
\end{array}\right]\ \ \begin{array}{l}
.\\
.\\
-R_{1}.
\end{array}$
$\left[\begin{array}{llll}
3 & 2 & 0 & 12\\
0 & 1 & -5 & 7\\
0 & -2 & 10 & 68
\end{array}\right]\ \ \begin{array}{l}
-R_{2}.\\
.\\
+2R_{2}.
\end{array}$
$\left[\begin{array}{llll}
. & . & . & .\\
0 & 1 & -5 & 7\\
0 & 0 & 0 & 82
\end{array}\right]\ \ \begin{array}{l}
.\\
.\\
.
\end{array}$
No need to continue, the system is inconsistent
(last row represents 0=82, which is not possible)
