Answer
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -2 \\ \frac{3}{4} \end{bmatrix} $
Work Step by Step
We will write the system of equations as follows:
$\begin{bmatrix} 3 & 4 \\ -5 & 8 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -3 \\ 16 \end{bmatrix} $
Next, we will find the inverse of the left matrix factor as follows:
$\dfrac{1}{(3)(8)-(4)(-5)}\begin{bmatrix} 8 & -4 \\ 5 & 3 \end{bmatrix} $
This yields to: $\begin{bmatrix} \frac{2}{11} & \frac{-1}{11} \\ \frac{5}{44} & \frac{3}{44} \end{bmatrix} $
Therefore, the value of $x,y$ can be calculated as:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} \frac{2}{11} & \frac{-1}{11} \\ \frac{5}{44} & \frac{3}{44} \end{bmatrix} \begin{bmatrix} -3 \\ 16 \end{bmatrix} $
After matrix multiplication, we get:
$\begin{bmatrix} x \\ y \end{bmatrix}=\begin {bmatrix} \frac{2}{11} (-3)-\frac{1}{11} (16) \\ \frac{5}{44}(-3)+ \frac{3}{44} (16)\end{bmatrix} = \begin{bmatrix} -2 \\ 3/4 \end{bmatrix} $
Hence, our result is:
$\begin{bmatrix} x \\ y \end{bmatrix}= \begin{bmatrix} -2 \\ \frac{3}{4} \end{bmatrix} $
