View this system as $\linearsystem{C}{\vect{b}}$, where $C$ is the $4\times 4$ matrix from Exercise MISLE.C28 and $\vect{b}=\colvector{-4\\4\\-20\\9}$.
Since $C$ was seen to be nonsingular in Exercise MISLE.C28 Theorem SNCM says the solution, which is unique by Theorem NMUS, is given by
\begin{equation*}
\inverse{C}\vect{b}=
\begin{bmatrix}
38 & 18 & -5 & -2\\
96 & 47 & -12 & -5\\
-39 & -19 & 5 & 2\\
-16 & -8 & 2 & 1
\end{bmatrix}
\colvector{-4\\4\\-20\\9}
=
\colvector{2\\-1\\-2\\1}
\end{equation*}
Notice that this solution can be easily checked in the original system of equations.