Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y \leq 7$

Question

Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y \leq 7$. This problem is found in the book How to Count by Beeler which contains no solutions, so I have no way of verifying the correct solution.

Answer 1

Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,\ldots,7.$