-16x +20x-8y=0
36=-18y-22x
Find x and y by using the elimination method
To solve the system of equations using the elimination method, we'll begin by multiplying the second equation by -2 to make the x terms cancel out.
Original equations:
-16x + 20x - 8y = 0 -> Equation 1
36 = -18y - 22x -> Equation 2
Multiply Equation 2 by -2:
-2(36) = -2(-18y - 22x)
-72 = 36y + 44x -> Equation 3
Now we'll add Equation 1 and Equation 3 to eliminate the x terms:
(-16x + 20x - 8y) + (-72 = 36y + 44x)
4x - 8y - 72 = 36y + 44x
Rearrange the equation:
4x - 44x - 8y - 36y = 72
Combine like terms:
-40x - 44y = 72 -> Equation 4
Now, we have a new equation:
-40x - 44y = 72 -> Equation 4
To further eliminate variables, we'll multiply Equation 4 by -1/4:
(-1/4)(-40x - 44y) = (-1/4)(72)
10x + 11y = -18 -> Equation 5
Now, we have two equations:
10x + 11y = -18 -> Equation 5
-40x - 44y = 72 -> Equation 4
To eliminate the y terms, we'll multiply Equation 4 by 11 and Equation 5 by 4:
11(-40x -44y ) = 11(72)
44x + 484y = 792 -> Equation 6
4(10x + 11y) = 4(-18)
40x + 44y = -72 -> Equation 7
Adding Equation 6 and Equation 7 to cancel the y terms:
(44x + 484y) + (40x + 44y ) = (792) + (-72)
84x = 720
Divide both sides by 84:
84x/84 = 720/84
x = 120/14
x = 60/7
Substitute this value of x into Equation 5 to find y:
10x + 11y = -18
10(60/7) + 11y = -18
600/7 + 11y = -18
Multiply both sides by 7:
600 + 77y = -126
77y = -726
y = -726/77
y = -66/7
Therefore, the solution to the system of equations is x = 60/7 and y = -66/7.