If x and y are positive integers and 3x+2y=13 what could be the value of y

If 'x' is a positive integer, then ...

- - the smallest 'x' could be is ' 1 '

- - the smallest '3x' could be is ' 3 '.

- - the greatest '2y' could be is (13 - 3) = 10

- - the greatest 'y' could be is ' 5 '.

So, ALL of the possible values of (x, y) are:

==> x=1, y=5

==> x=3, y=2

And that's all. There are no other possibilities.