Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} \frac{7}{2} \\ -1 \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 2 & -3 \\ 2 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 10 \\ 5 \end{bmatrix} $
Next, we will find the inverse of the left matrix factor as follows:
$\dfrac{1}{(2)(2)-(-3)(2)}\begin{bmatrix} 2 & 3 \\ -2 & 2 \end{bmatrix} $
This yields to: $\begin{bmatrix} \frac{1}{5} & \frac{3}{10} \\ -\frac{1}{5} & \frac{1}{5} \end{bmatrix} $
Therefore, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} \frac{1}{5} & \frac{3}{10} \\ -\frac{1}{5} & \frac{1}{5} \end{bmatrix} \begin{bmatrix} 10 \\ 5 \end{bmatrix} $
After matrix multiplication, we get:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} \frac{7}{2} \\ -1 \end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} \frac{7}{2} \\ -1 \end{bmatrix} $
