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

Let's start by solving the second equation for b:
2a + b = 7
b = 7 - 2a
Now, substitute this expression for b into the first equation:
3a - 2(7 - 2a) = 14
3a - 14 + 4a = 14
7a - 14 = 14
7a = 28
a = 4

Now that we have found the value of a, we can substitute it back into one of the original equations to solve for b:
2(4) + b = 7
8 + b = 7
b = -1

Therefore, the solution to the system of equations is:
a = 4
b = -1