How many pairs of whole numbers have a sum of 40

Let

and

represent the pairs of whole numbers that have a sum of 40.

This implies that,



This a single linear equation in two variable. To solve this kind of equation, we make one variable the subject. Say,



Since,

is a whole number, the domain of the above function is the set of whole numbers.

In order to get a solution, we choose a value for x and then solve for corresponding value of y.

If




This means,



Hence,



is one possible solution.

Since the set of whole numbers we can choose for

is infinitely many,