To solve this system of equations, we can use the elimination method.

First, let's multiply the first equation by 2 to make the coefficient of y the same as the second equation:

2(x - 2y) = 6
2x - 4y = 6

Now, we have the two equations:

2x - 4y = 6
-0.5x + 2y = -1.5

Adding the two equations together:

2x - 4y - 0.5x + 2y = 6 - 1.5
1.5x - 2y = 4.5

Now, isolating y in this new equation:

1.5x - 2y = 4.5
-2y = -1.5x + 4.5
y = 0.75x - 2.25

Now, substitute this value of y back into either of the original equations to solve for x. Let's use the first equation:

x - 4(0.75x - 2.25) = 3
x - 3x + 9 = 3
-2x + 9 = 3
-2x = -6
x = 3

Now that we have x, we can substitute it back into the equation to solve for y:

-0.5(3) + 2y = -1.5
-1.5 + 2y = -1.5
2y = 0
y = 0

Therefore, the solution to the system of equations is x = 3, y = 0.