In order to solve this system, we can use the following steps:
[tex]\begin{gathered} AX=B\\ \\ A^{-1}AX=A^{-1}B\\ \\ IX=A^{-1}B\\ \\ X=A^{-1}B \end{gathered}[/tex]
So, to find the solution, let's multiply the inverse matrix with matrix B, which is the matrix of independent terms:
[tex]\begin{gathered} B=\begin{bmatrix}{-3} & {} \\ 8{} & {}\end{bmatrix}\\ \\ \\ \\ X=A^{-1}B=\begin{bmatrix}{11} & {-7} \\ {-3} & {2}\end{bmatrix}\begin{bmatrix}{-3} & {} \\ 8{} & {}\end{bmatrix}=\begin{bmatrix}11\cdot(-3)+(-7)\cdot8 & {} \\ -3\cdot(-3)+2\cdot8{} & {}\end{bmatrix}=\begin{bmatrix}{-33-56} & {} \\ {9+16} & {}\end{bmatrix}\\ \\ =\begin{bmatrix}-89 & {} \\ 25{} & {}\end{bmatrix} \end{gathered}[/tex]
Therefore the solution is (-89, 25).
