Answer:
The system of equations is:
-5x + 9y = -9
5x - 8y = 4
The determinant of the coefficients is:
D = |-5 9|
| 5 -8|
D = (-5)(-8) - (9)(5) = 40 - 45 = -5
The determinant of x is found by replacing the x-coefficients with the constants:
Dx = |-9 9|
| 4 -8|
Dx = (-9)(-8) - (9)(4) = 72 - 36 = 36
The determinant of y is found by replacing the y-coefficients with the constants:
Dy = |-5 -9|
| 5 4|
Dy = (-5)(4) - (-9)(5) = -20 + 45 = 25
Using Cramer's Rule:
x = Dx/D = 36/-5 = -7.2
y = Dy/D = 25/-5 = -5
Therefore, the solution to the system is x = -7.2 and y = -5.
Hope this helps!