3. Solve the system of two equations using elimination with multiplication.
4x - 6y = -48
-2x + 4y = 30
To solve this system using elimination with multiplication, we need to multiply one or both of the equations by a constant so that when we add or subtract the equations, one of the variables will be eliminated.
Let's first multiply the second equation by 2 to make the coefficients of the x terms the same but with opposite signs:
2(-2x + 4y) = 2(30)
-4x + 8y = 60
Now, we have the system:
4x - 6y = -48
-4x + 8y = 60
When we add these equations together, the x terms will be eliminated:
(4x - 6y) + (-4x + 8y) = -48 + 60
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. Let's use the first equation:
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.