Consider this scenario: "$10,000 is to be split into three bank accounts, paying 4%, 6% and 8% simple yearly interest. At the end of one year, the sum of interest is $575. Give some example how the money can be split to obtain this sum of interest." This is a two equation, three variable system, and it will not have one solution, but many. Now, using only algebra, try to find some solutions. What do you notice each time you start the problem from scratch each time (for example, do you find yourself repeating steps)? Are some of your solutions meaningless (e.g. negative)? Now, reconsider this as a 2x4 RREF matrix. Discuss how this form is much "cleaner" in generating solutions. In fact, can you determine bounds on the parameter that will ensure meaningful (all variables non-negative) solutions?