Question

Solve the system of two equations using elimination with multiplication. 4x−6y=−48 −2x+4y=30 (1 point) Responses (3, 9) left parenthesis 3 comma 9 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, 6)

Answer 1

To solve the system of equations using elimination with multiplication, we need to multiply one or both equations by a constant so that when we add or subtract the equations, one of the variables will cancel out.

Let's first multiply the second equation by 2 to eliminate the x terms:

2(-2x+4y)=2(30)
-4x+8y=60

Now we have the following system of equations:

4x-6y=-48
-4x+8y=60

When we add these two equations together, the x terms will cancel out:

(4x-4x) + (-6y+8y) = (-48+60)
0 + 2y = 12
2y = 12

Now we can solve for y by dividing both sides of the equation by 2:

2y/2 = 12/2
y = 6

We have found the value of y, which is 6. Now we can substitute this value back into one of the original equations to solve for x. Let's use the first equation:

4x - 6(6) = -48
4x - 36 = -48

To isolate x, we add 36 to both sides of the equation:

4x - 36 + 36 = -48 + 36
4x = -12

Now we can solve for x by dividing both sides of the equation by 4:

4x/4 = -12/4
x = -3

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