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

First, let's solve the first equation for x:

0.5x + 3y = 1.5
0.5x = 1.5 - 3y
x = 3 - 6y

Now, substitute this expression for x into the second equation:

0.5(3 - 6y) - 2y = 4
1.5 - 3y - 2y = 4
1.5 - 5y = 4
-5y = 2.5
y = -0.5

Now that we have found the value of y, we can substitute it back into the first equation to find x:

0.5x + 3(-0.5) = 1.5
0.5x - 1.5 = 1.5
0.5x = 3
x = 6

Therefore, the solution to the system of equations is x = 6 and y = -0.5.