Suppose you wanted to find the solutions to the following set of equations:

Xavier and Yolanda both bake pies. In one hour, the pair create a total of 5 pies. If Xavier works for 3 hours and Yolanda works for 4 hours, the pair can create a total of 17 pies. How many pies does each produce per hour?

This tutorial discusses how to solve such problems, and a clever trick to make even the hardest linear simultaneous equations easy.