The augmented matrix for the given linear system and its row-reduced form are:
\begin{align*}
\begin{bmatrix}
1 & 2 & 3 & 1\\
2 & -1 & 1 & 2\\
1 & -8 & -7 & 1\\
0 & 1 & 1 & 0
\end{bmatrix}
\rref
\begin{bmatrix}
\leading{1} & 0 & 1 & 1\\
0 & \leading{1} & 1 & 0\\
0 & 0 & 0 & 0\\
0 & 0 & 0 & 0
\end{bmatrix}.
\end{align*}
For this system, $n = 3$ and $r = 2$.
Since it is a consistent system by Theorem RCLS, Theorem CSRN guarantees an infinite number of solutions. An equivalent system is
\begin{align*}
x_1 &= 1 - x_3\\
x_2 &= -x_3,
\end{align*}
where $x_3$ is any scalar. So we can express the solution set as
\begin{align*}
\setparts{\colvector{1 - x_3\\ -x_3\\x_3}}{x_3\in\complexes}
\end{align*}