Question

15 POINTS!! NEED ANSWER FAST
Use a matrix to find the solution to the system of equations
{-8x-8y=-16
6x-9y=-108

Answer choices:
(-6 8)
(6, 8)
(8 -6)
(6, -8)

Answer 1

Given that,

The equations are,

$-8x-8y=-16$...(I)

$6x-9y=-108$.....(II)

We need to simplify the equation

Using equation (I)

$-8x-8y=-16$

Now, divided the equation by -8

$x+y=2$....(III)

Using equation (II)

$6x-9y=-108$

Now, divided the equation by 3

$2x-3y=-36$....(IV)

We write the equations in matrix form

From equation (III) and (IV)

$\left[\begin{array}{ccc}1&1\\2&-3\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}2\\-36\end{array}\right]$

We need to calculate the determine of the matrix

Using formula of determine

$D=(1)(-3)-(1)(2)$

$D=-5$

We need to calculate the value of x and y

Use cramer's Rule

For value of x,

$x=\dfrac{1}{D}det(\left[\begin{array}{ccc}2&1\\-36&-3\end{array}\right])$

Put the value of D

$x=\dfrac{1}{-5}\times(-6+36)$

$x=-6$

For value of y,

$y=\dfrac{1}{D}det(\left[\begin{array}{ccc}1&2\\2&-36\end{array}\right])$

Put the value of D

$y=\dfrac{1}{-5}\times(-36-4)$

$y=8$

Hence, The value of x and y is -6 and 8

(A) is correct option.