Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30 (
To solve this system of equations using elimination with multiplication, we need to make the coefficients of either the x or y terms the same in both equations. Let's focus on making the coefficients of the y terms the same in both equations by multiplying the first equation by 2 and the second equation by 3:
2(4x - 6y) = 2(-48)
3(-2x + 4y) = 3(30)
This gives us:
8x - 12y = -96
-6x + 12y = 90
Now, we can add these two equations together to eliminate the y term:
(8x - 12y) + (-6x + 12y) = -96 + 90
2x = -6
x = -3
Now, substitute the value of x back into either of the original equations. We will use the first equation:
4(-3) - 6y = -48
-12 - 6y = -48
-6y = -36
y = 6
Therefore, the solution to the system of equations is x = -3 and y = 6.