First, we will solve one equation for one variable in terms of the other variable. Let's solve the first equation for y in terms of x:
4x - 2y = -1
-2y = -4x - 1
y = 2x + 1/2
Now we can substitute this expression for y into the second equation:
8x - 4y = -2
8x - 4(2x + 1/2) = -2
8x - 8x - 2 = -2
-2 = -2
This is a true statement, which means that the system of equations has infinitely many solutions. In other words, any value of x will satisfy the system of equations.
So the answer is that the system of equations has infinitely many solutions.