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,

The answer is “faster”.