Answer
No Solution.
Work Step by Step
To solve the system $\begin{cases}-x+3y=6 \\ 3x-9y=9 \\ \end{cases},$ we perform elementary row operations on the corresponding augmented matrix to obtain an equivalent matrix with $1s$ along the main diagonal (if possible).
The corresponding augmented matrix is
$$\left[
\begin{array}{cc|c}
-1 & 3 & 6 \\
3 & -9 & 9\\
\end{array}
\right].$$
We multiply Row_1 by $-1$ to obtain the equivalent matrix
$$\left[
\begin{array}{cc|c}
1 & -3 & -6 \\
3 & -9 & 9\\
\end{array}
\right].$$
We replace Row_2 with Row_2-3*Row_1 to obtain the equivalent matrix
$$\left[
\begin{array}{cc|c}
1 & -3 & -6 \\
0 & 0 & 27\\
\end{array}
\right].$$
Now, we see in Row_2 that every entry but the last entry is a zero. This means the system of equations corresponding to this matrix is inconsistent (i.e., has no solutions).
To see this, we form the system of equations corresponding to this matrix:
$$\begin{cases}x-3y=-6 \\ 0=27 \\ \end{cases}.$$
We see $0=27$ is false for all values of $x$ and/or $y$. So this system of equations has no solutions.