We're told that 3x and y must add to 10.
Since x and y are positive integers, we can see that the maximum value of x is 3, which means there are only three possible values of 3: x = 1, x = 2, and x =3
Let's examine all three possible cases:

If x = 1, then y = 7
If x = 2, then y = 4
If x = 3, then y = 1

So, the three possible integer solutions are (1, 7), (2, 4) and (3, 1)

Answer: C