Question

Solve the following using Elimination:
7x + 8y = -9
-4x+9y=-22

Answer 1

To solve these equations using elimination, we will multiply the first equation by 4 and the second equation by 7 to eliminate the x term.

Multiplying the first equation by 4:
4(7x + 8y) = 4(-9)
28x + 32y = -36

Multiplying the second equation by 7:
7(-4x+9y) = 7(-22)
-28x + 63y = -154

Now, we can add these two equations together to eliminate the x term:
(28x + 32y) + (-28x + 63y) = (-36) + (-154)
28x + 32y - 28x + 63y = -36 - 154
95y = -190
y = -190/95
y = -2

Substitute the value of y back into one of the original equations (let's use the first one) to solve for x:
7x + 8(-2) = -9
7x - 16 = -9
7x = 7
x = 7/7
x = 1

Therefore, the solution to the system of equations is x = 1 and y = -2.