Answer
See below
Work Step by Step
According to Cramer's Rule, the solution to $2 \times 2$ system $Ax=b$ is given by:
$$x_k=\frac{\det(B_k)}{\det(A)}$$
From the given matrix, we have:
$A=\begin{bmatrix}
-3 &1&-3 & -9\\1 & -2 &0&-4\\0 &0&2&1\\1&1&0&1
\end{bmatrix}\\
B_4=\begin{bmatrix}
-3 &1&-3 & -3\\1 & -2 &0&1\\0 &0&2&-1\\1&1&0&0
\end{bmatrix} $
The determinants are:
$\det(A)=-3(-4-8)-1(2-3+18)+(-1)(36-8-6)=-3\\
\det(B_4)=-3(-2)-1.9-1.16=-19$
Hence, $x_4=\frac{19}{3}$
