Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -2 \\ 4 \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -8 \\ -2 \end{bmatrix} $
Next, we will find the inverse of the left matrix factor as follows:
$\dfrac{1}{(2)(1)+(1)(3)}\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix} $
This yields to: $\begin{bmatrix} 1/5 & 1/5 \\ -3/5 & 2/5 \end{bmatrix} $
Therefore, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 1/5 & 1/5 \\ -3/5 & 2/5 \end{bmatrix} \begin{bmatrix} -8 \\ -2 \end{bmatrix} $
After matrix multiplication, we get:, $\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -2 \\ 4 \end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -2 \\ 4 \end{bmatrix} $
