The coefficient matrix and vector of constants for the system are
\begin{align*}
\begin{bmatrix}
1 & 1 & 3 & 1\\
-2 & -1 & -4 & -1\\
1 & 4 & 10 & 2\\
-2 & 0 & -4 & 5
\end{bmatrix}&&
\vect{b}=\colvector{5\\-7\\9\\9}
\end{align*}
$\inverse{A}$ can be computed by using a calculator, or by the method of Theorem CINM.
Then Theorem SNCM says the unique solution is
\begin{equation*}
\inverse{A}\vect{b}=
\begin{bmatrix}
38 & 18 & -5 & -2\\
96 & 47 & -12 & -5\\
-39 & -19 & 5 & 2\\
-16 & -8 & 2 & 1
\end{bmatrix}
\colvector{5\\-7\\9\\9}
=
\colvector{1\\-2\\1\\3}
\end{equation*}