To solve the system of equations using the elimination method, we can eliminate one of the variables by multiplying one or both of the equations by a constant. Let's eliminate x by multiplying the first equation by -4:
-4x - 4y = -16
4x + 3y = 24
Adding the two equations eliminates x:
-y = 8
Solving for y gives:
y = -8
Substituting y = -8 into the first equation gives:
x + (-8) = 4
Solving for x gives:
x = 12
Therefore, the solution to the system of equations is x = 12 and y = -8.