Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Skill Practice - Page 214: 18

$$X=\begin{pmatrix}2&\frac{13}{3}&-4\\ 7&\frac{40}{3}&-10\end{pmatrix}$$

Isolating X by taking the inverse of the matrix, we find: $$\begin{pmatrix}-5&2\\ -9&3\end{pmatrix}X=\begin{pmatrix}4&5&0\\ 3&1&6\end{pmatrix} \\ X=\begin{pmatrix}-5&2\\ -9&3\end{pmatrix}^{-1}\begin{pmatrix}4&5&0\\ 3&1&6\end{pmatrix} \\ X=\begin{pmatrix}2&\frac{13}{3}&-4\\ 7&\frac{40}{3}&-10\end{pmatrix}$$