Question

Solve the system of two equations using elimination with multiplication
4x-6y=-48
-2x+4y=30

Answer 1

To solve the system of equations using elimination with multiplication, we need to eliminate one of the variables by multiplying one or both of the equations.

First, let's eliminate the x variable. To do this, we need to multiply the second equation by 2 to make the x term in both equations cancel each other out:

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

Now we have the system of equations:
4x - 6y = -48
-4x + 8y = 60

Adding the two equations together:

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

2y = 12
y = 12/2
y = 6

Substituting this value of y back into one of the original equations, we can 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 = -3 and y = 6.