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

First, let's solve the second equation for y in terms of x:

2x - y = 12
y = 2x - 12

Next, substitute this expression for y into the first equation:

3x + 2(2x - 12) = 34
3x + 4x - 24 = 34
7x - 24 = 34
7x = 58
x = 58/7
x = 8.2857

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

2(8.2857) - y = 12
16.5714 - y = 12
-y = -4.5714
y = 4.5714

Therefore, the solution to the system of equations is x = 8.2857 and y = 4.5714.