To solve this system of equations, we will first isolate one variable in terms of the other from one of the equations and then substitute it into the other equation.

From the second equation, we have:

x/y + 1 = 3/2
x/y = 3/2 - 1
x/y = 1/2

Now, we can substitute this value of x/y into the first equation:

x^2 + xy = 3/4
(x)(x/2) + x(1/2) = 3/4
(x^2)/2 + x/2 = 3/4
Multiplying by 2 to get rid of the fractions:
x^2 + x = 3/2

Now, we have the equation x^2 + x = 3/2. Let's solve this quadratic equation.

x^2 + x - 3/2 = 0

Using the quadratic formula:
x = [ -1 ± sqrt(1 + 24) ] / 2
x = [ -1 ± sqrt(25) ] / 2
x = [ -1 ± 5 ] / 2

So, the possible values for x are:
x = (5-1) / 2 = 4 / 2 = 2
x = (1-5) / 2 = -4 / 2 = -2

Now that we have the possible values for x, we can find the corresponding values for y using x/y = 1/2:

If x = 2:
2/y = 1/2
y = 4

If x = -2:
-2/y = 1/2
y = -4

Therefore, the solutions to the system of equations are:
x = 2, y = 4
or
x = -2, y = -4