Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30(1 point)
Responses
(−33,−9)
left parenthesis negative 33 comma negative 9 right parenthesis
(3, 9)
left parenthesis 3 comma 9 right parenthesis
(−3, 6)
left parenthesis negative 3 comma 6 right parenthesis
(−21,−6)
To solve the system of equations using elimination with multiplication, we need to eliminate one variable by manipulating the equations and then solve for the remaining variable.
First, let's multiply the second equation by 2 to make the coefficients of x in both equations equal:
2(-2x + 4y) = 2(30)
-4x + 8y = 60
Now, we have the system of equations:
4x - 6y = -48
-4x + 8y = 60
Adding these two equations together eliminates the variable x:
(4x - 6y) + (-4x + 8y) = -48 + 60
-6y + 8y = 12
2y = 12
y = 12/2
y = 6
Substituting y = 6 back into one of the original equations to solve for x:
4x - 6(6) = -48
4x - 36 = -48
4x = -48 + 36
4x = -12
x = -12/4
x = -3
Therefore, the solution to the system of equations is (x, y) = (-3, 6). So the correct answer is (−3, 6).