Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} 3 \\ -5 \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 1 & 3 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -12 \\ 11 \end{bmatrix} $
Next, we will find the inverse of the left matrix factor as follows:
$\dfrac{1}{(1)(-1)-(3)(2)}\begin{bmatrix} -1 & -3 \\ -2 & 1 \end{bmatrix} $
This yields to: $\begin{bmatrix} 1/7 & 3/7 \\ 2/7 & -1/7 \end{bmatrix} $
Therefore, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 1/7 & 3/7 \\ 2/7 & -1/7 \end{bmatrix} \begin{bmatrix} -12 \\ 11 \end{bmatrix} $
After matrix multiplication, we get:, $\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 1/7 (-12) + (3/7)(11) \\ 2/7 (-12)-(1/7)(11) \end{bmatrix} = \begin{bmatrix} 3 \\ -5 \end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} 3 \\ -5 \end{bmatrix} $
