let

x = the number of bicycles

y = the number of tricycles

there are a total of 24 seats

x + y = 24 since there is 1 sit per bicycle and 1 sit per tricycle

there are a total of 61 wheels

2x + 3y = 61 since every bicycle has 2 wheels and every tricycle has 3 wheels

by solving the system of equations

x + y = 24

2x + 3y = 61

we find

x = 11 bicycles

y = 13 tricycles

there are 11 bicycles and 13 tricycles in the shop.