Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Skill Practice - Page 214: 16

$$X=\begin{pmatrix}\frac{19}{6}&\frac{7}{6}\\ \frac{29}{12}&\frac{5}{12}\end{pmatrix}$$

Isolating X by taking the inverse of the matrix, we find: $$\begin{pmatrix}-3&6\\ 1&2\end{pmatrix}X=\begin{pmatrix}5&-1\\ 8&2\end{pmatrix} \\ X=\begin{pmatrix}-3&6\\ 1&2\end{pmatrix}^{-1}\begin{pmatrix}5&-1\\ 8&2\end{pmatrix} \\ X=\begin{pmatrix}\frac{19}{6}&\frac{7}{6}\\ \frac{29}{12}&\frac{5}{12}\end{pmatrix}$$