Question

Please explain

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

(-6,8)
(6,8)
(8,-6)
(6,-8)

Answer 1

Isolate x for -8x-8y=-16
the answer will be (8,-6)

Answer 2

Explanation:

the right answer is a (-6,8) where x=-6 and y=8

We're going to use Cramer's rule to resolve this question.

First of all, we're going to give a number to the equations:

(1) -8x-8y=-16

(2) 6x-9y=-108

where constant 1=c1=-16 and the constant 2=c2=-108

now we need to find the next determinants:

D: system determinant,Dx and Dy.

now we're going to find "D."

for that, we're going to take the coefficients of x and y in (1) and (2)

x y

D=
`\f\left[\begin{array}{ccc}-8&-8\\6&-9\end{array}\right]`

this is how we need to put the matrix, using the numbers next to x and y in the (1) and (2) equation.

to solve this matrix, we need to multiplicate in X, and subtract the results; so for D we have:

(-8*-9)-(6*-8)

72-(-48)=

72+48=120

now we're doing the same process to find Dx and Dy, but in each case, we're going to replace x or y with the constants (the constants are the numbers right to the "=")

to find Dx we're going to use the values of c1 and c2 instead of x

C1&2 y

Dx=
`\f\left[\begin{array}{ccc}-16&-8\\-108&-9\end{array}\right]`

Now we do the same as with D

(-16*-9)-(-108*-8)=

144-(864)

144-864=-720

and now for Dy=

x C1&2

Dy=
`\f\left[\begin{array}{ccc}-8&-16\\6&-108\end{array}\right]`

= (-8*-108)-(6*-16)=

864-(-96)=

864+96=960

now the last step is to find x and y .

x=
`(Dx)/(D)` Y=
`(Dy)/(D)`

x= -720/120=-6

y=960/120=8

x=-6 y= 8

answer = (-6,8)