Solve the system by the elimination method.
3x−5y=4
−9x+3y=−24
(1 point)
Responses
(3,1)
open paren 3 comma 1 close paren
(8,4)
open paren 8 comma 4 close paren
(2, −2)
(2, −2)
(1, −1)
(1, −1)
To solve the system by the elimination method, we can multiply the first equation by 3 and the second equation by 5 to eliminate the x term:
3(3x-5y) = 3(4) simplifies to 9x - 15y = 12
5(-9x+3y) = 5(-24) simplifies to -45x + 15y = -120
Now we can add these two equations together:
(9x - 15y) + (-45x + 15y) = 12 + (-120)
9x - 45x - 15y + 15y = -108
-36x = -108
x = -108 / -36
x = 3
Substitute x = 3 into the first equation to solve for y:
3(3) - 5y = 4
9 - 5y = 4
-5y = 4 - 9
-5y = -5
y = -5 / -5
y = 1
Therefore, the solution to the system of equations is (3, 1).