Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -\frac{1}{2} \\ \frac{2}{3} \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 6 & 9 \\ -8 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 3 \\ 6 \end{bmatrix} $
Next, we will find the inverse of the left matrix factor as follows:
$\dfrac{1}{(6)(3)-(9)(-8)}\begin{bmatrix} 3 & -9 \\ 8 & 6 \end{bmatrix} $
This yields to: $\begin{bmatrix} \frac{1}{30} & -\frac{1}{10} \\ \frac{4}{45} & \frac{3}{45} \end{bmatrix} $
Therefore, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} \frac{1}{30} & -\frac{1}{10} \\ \frac{4}{45} & \frac{3}{45} \end{bmatrix} \begin{bmatrix} 3 \\ 6 \end{bmatrix} $
After matrix multiplication, we get:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -\frac{1}{2} \\ \frac{2}{3} \end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -\frac{1}{2} \\ \frac{2}{3} \end{bmatrix} $
