Answer the following questions. Be prepared to explain your answers to the class.

Linear Combinations

Example: Rosa wants to buy a piece of candy from Jamal for ten cents.  Rosa only has quarters.  Jamal checks his pocket and finds he has only dimes.  Explain how Rosa can buy the candy from Jamal.






Definition.  A linear combination of two numbers is a sum of multiples of those numbers. In symbols, a linear combination of integers a and b is an expression of the form na+mb, where n and m are integers.

You can create all linear combinations of, for example, 25 and 10, by starting at 0 and repeatedly adding or subtracting either 25 or 10 at each step.