Suppose you intend to spend $60 buying books. Hardback books cost $12 and paperback cost $5. How many books of each type can you buy?
We have two solutions:
A) All money ($60) are spent on 12 paperbacks at $5 each
B) All money ($60) are spent on 5 hardbacks at $12 each
Let's approach this as a problem with two unknown:
There is only one equation that these two variables satisfy:
Generally speaking, one equation is insufficient to find a solution for two variables among all real numbers. However, we should not look for real numbers as solutions, only for positive integer ones.
the number of books at $12 (that is,
So, we have two solutions: