Use the elimination method to solve the follow system of equations.9x−7y=22x+3y=−24This question requires you to show your work.(1 point)Responses(3,−9)open paren 3 comma negative 9 close paren(4, 2)(4, 2)(0,−8)open paren 0 comma negative 8 close paren(−3,−7)open paren negative 3 comma negative 7 close paren
To solve the system of equations using the elimination method, we can multiply the second equation by 3 to make the coefficients of y in both equations equal:
9x - 7y = 22
6x + 9y = -72
Next, we can add the two equations together to eliminate y:
9x - 7y + 6x + 9y = 22 - 72
15x + 2y = -50
Now, we can use this new equation along with the first equation to solve for x:
15x + 2y = -50 (multiply the first equation by 2)
18x - 14y = 44
Now, add the two equations together:
15x + 2y + 18x - 14y = -50 + 44
33x - 12y = -6
Solve for x:
33x - 12y = -6
33x = 12y - 6
33x = 12(-9) - 6
33x = -108 - 6
33x = -114
x = -114 / 33
x = -3
Now that we have x = -3, we can substitute this back into the first equation to solve for y:
9(-3) - 7y = 22
-27 - 7y = 22
-7y = 49
y = 49 / -7
y = -7
Therefore, the solution to the system of equations is (x, y) = (-3, -7).