You know you have the equation: 23 = 3*Tricycles + 2*Bicycles

Since you know each has at least two, take these out.

This leaves you with:

13 = 3*(Remaining Tricycles) + 2*(Remaining Bicycles)

Since the number is small, trial and error works best. You have 2 possible combinations to make 13.

1. 1 tricycle, 5 bicycles

2. 3 tricycles, 2 bicycles

Since we know there are more bicycles, option number 1 is correct. Now add back in the first 2, leaving you with:

3 tricycles and 7 bicycles.