Solve the system of two equations using elimination with multiplication.
4x - 6y = - 48
- 2x + 4y = 30
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 is eliminated.
First, let's multiply the second equation by 2 so that the coefficients of y become 8 and -8 when added to the first equation:
4x - 6y = -48
-4x + 8y = 60
Now, add the two equations together:
0x + 2y = 12
2y = 12
y = 6
Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x:
4x - 6(6) = -48
4x - 36 = -48
4x = -12
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 6.