Question

Brainly use a matrix to find the solution to the system of equations -8x-8y=-16 6x-9y=-108

Answer 1

We want to use a matrix to solve
-8x - 8y = -16
6x - 9y = -108

Before solving, simplify the equations as follows:
Divide the first equation by -8 to obtain
x + y = 2             (1)
Divide the second equation by 3 to obtain
2x - 3y = -36       (2)

In matrix form, the equations are
$\begin{bmatrix}1&1\\2&-3\end{bmatrix} \begin{\bmatrix} x\\y\end{bmatrix}=\begin{bmatrix}2 \\ -36 \end{bmatrix}$

The determinant of the matrix is
D = (1)(-3) - (1)(2) = -5

Use Cramer's Rule.
$x = \frac{1}{D} det(\begin{bmatrix}2&1\\-36&-3 \end{bmatrix} ) = \frac{1}{-5} (-6+36) = -6$
Similalrly, 
$y= \frac{1}{-5} det(\begin{bmatrix} 1&2\\2&-36\end{bmatrix} ) = \frac{1}{-5}(-36-4) =8$

Answer:  (-6, 8)  or x = -6, y = 8