Question 42·Hard·Linear Equations in Two Variables

At a community farm, strawberries are packed in small crates that hold 3 kilograms each, and watermelons are packed in large crates that hold 7 kilograms each. A shipment contains a combined total of 116 kilograms of strawberries and watermelons. If $x$ represents the number of small crates of strawberries and $y$ represents the number of large crates of watermelons, the relationship between $x$ and $y$ can be written as

If both $x$ and $y$ must be whole numbers, what is the greatest possible value of $y$?