Answer
No solution or $\varnothing$.
Work Step by Step
The given system of equations is
$2x-3y=8$
$-6x+9y=4$
The augmented matrix is
$\Rightarrow \left[\begin{array}{cc|c}
2 & -3 & 8\\
-6 & 9 & 4
\end{array}\right]$
Perform $R_1\rightarrow R_1/2$.
$\Rightarrow \left[\begin{array}{cc|c}
2/2 & -3/2 & 8/2\\
-6 & 9 & 4
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & -3/2 & 4\\
-6 & 9 & 4
\end{array}\right]$
Perform $R_2\rightarrow R_2+6 R_1$.
$\Rightarrow \left[\begin{array}{cc|c}
1 & -3/2 & 4\\
-6+6(1) & 9+6(-3/2) & 4+6(4)
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & -3/2 & 4\\
0 & 0 & 28
\end{array}\right]$
Use back substitution in the second row.
$\Rightarrow 0x+0y=28$
There are no values of $x$ and $y$ for which the above equation satisfies.
Hence, there is no solution.
The solution set is no solution or $\varnothing$.
