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

1 answer:

8 0

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

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