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 equal in both equations.
In this case, we can do this by multiplying the first equation by 2 and the second equation by 3 to make the coefficients of x in both equations equal:
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 y:
8x - 12y + (-6x + 12y) = -96 + 90
2x = -6
x = -3
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
4x - 6y = -48
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.