Answer
No solution
Work Step by Step
We are given the system:
$\begin{cases}
3x-y=9\\
2y-6x=7
\end{cases}$
$\begin{cases}
3x-y=9\\
-6x+2y=7
\end{cases}$
We will use the addition method. Multiply Equation 1 by 2 and add it to Equation 2 to eliminate $y$ and determine $x$:
$\begin{cases}
2(3x-y)=2(9)\\
-6x+2y=7
\end{cases}$
$\begin{cases}
6x-2y=18\\
-6x+2y=7
\end{cases}$
$6x-2y-6x+2y=18+7$
$0=25$
We got a false statement, therefore the system has no solution.