Question

Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30(1 point)
Responses

(−3, 6)
left parenthesis negative 3 comma 6 right parenthesis

(−21,−6)
left parenthesis negative 21 comma negative 6 right parenthesis

(−33,−9)
left parenthesis negative 33 comma negative 9 right parenthesis

(3, 9)

Answer 1

To solve the system of equations using elimination with multiplication, we can multiply the first equation by 2 and the second equation by 3 in order to create opposite coefficients for the x-term.

First equation: 4x - 6y = -48
Multiply by 2: 8x - 12y = -96

Second equation: -2x + 4y = 30
Multiply by 3: -6x + 12y = 90

Now, we can add the two new equations to eliminate the y-term:
(8x - 12y) + (-6x + 12y) = (-96) + 90
2x = -6
Divide by 2:
x = -3

Substitute this value back into one of the original equations (let's use the first equation):
4(-3) - 6y = -48
-12 - 6y = -48
-6y = -36
Divide by -6:
y = 6

Therefore, the solution to the system of equations is (x, y) = (-3, 6).