Use the elimination method to solve the follow system of equations.
9x−7y=22
x+3y=−24
This question requires you to show your work.
Responses
(4, 2)
(4, 2)
- no response given
(3,−9)
open paren 3 comma negative 9 close paren - no response given
(−3,−7)
open paren negative 3 comma negative 7 close paren - correct
(0,−8)
To solve this system of equations using the elimination method, we first need to eliminate one of the unknown variables by adding or subtracting the equations.
Let's eliminate the variable x.
Multiplying the second equation by 9, we get:
9(x + 3y) = 9(-24)
9x + 27y = -216
Now we have the following system of equations:
9x - 7y = 22
9x + 27y = -216
Subtracting the first equation from the second equation to eliminate x, we get:
(9x + 27y) - (9x - 7y) = -216 - 22
27y + 7y = -238
34y = -238
y = -7
Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
9x - 7(-7) = 22
9x + 49 = 22
9x = -27
x = -3
Therefore, the solution to the system of equations is x = -3 and y = -7, or (-3, -7).