Answer
(a) $ \begin{bmatrix} 4&-3\\3&-2 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix}= \begin{bmatrix} 10\\30 \end{bmatrix}$
(b) $(70,90)$
Work Step by Step
(a) Define the following matrices:
$\begin{array} \\A= \\ \end{array} \begin{bmatrix} 4&-3\\3&-2 \end{bmatrix},
\begin{array} \\X= \\ \end{array} \begin{bmatrix} x\\y \end{bmatrix},
\begin{array} \\B= \\ \end{array} \begin{bmatrix} 10\\30 \end{bmatrix}$
We can define the matrix equation equivalent to the system as $AX=B$
$ \begin{bmatrix} 4&-3\\3&-2 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix}= \begin{bmatrix} 10\\30 \end{bmatrix}$
(b) Use the inverse formula, we can get
$\begin{array} \\A^{-1}=\frac{1}{-8+9} \\ \end{array} \begin{bmatrix} -2&3\\-3&4 \end{bmatrix}$
$\begin{array} \\X=A&{-1}B= \\ \end{array} \begin{bmatrix} -2&3\\-3&4 \end{bmatrix}
\begin{bmatrix} 10\\30 \end{bmatrix}=\begin{bmatrix} 70\\90 \end{bmatrix}$
Thus, the solution is $(70,90)$
