But, 3 vans and 2 cars isn't the only valid solution, unless you assume every vehicle has to be full.  Four vans and 1 car works, and a previous poster gave the example of 5 vans, which also works.  The fact that there are multiple valid solutions when you remove the constraint that each vehicle should be as full as possible makes me think this is a lousy example for illustrating systems of equations.  It is, however, a great problem for teaching combinatorics, since, for each solution, you can count the number of ways to fill the vehicles, and thus the total number of distinct ways to transport the 31 people.