Answer:
Step-by-step 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= [tex]\f\left[\begin{array}{ccc}-8&-8\\6&-9\end{array}\right][/tex]
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= [tex]\f\left[\begin{array}{ccc}-16&-8\\-108&-9\end{array}\right][/tex]
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= [tex]\f\left[\begin{array}{ccc}-8&-16\\6&-108\end{array}\right][/tex]
= (-8*-108)-(6*-16)=
864-(-96)=
864+96=960
now the last step is to find x and y .
x= [tex]\frac{Dx}{D}[/tex] Y= [tex]\frac{Dy}{D}[/tex]
x= -720/120=-6
y=960/120=8
x=-6 y= 8
answer = (-6,8)
