You keep a number of lizards, mice and peacocks as pets. There are a total of 108 legs and 30 tails in your menagerie. You have twice as many mice as lizards. How many of each creature do you have?

(Chris Black) Let l, m, p denote the number of lizards, mice and peacocks. Then the statements from the problem yield the equations

4l + 4m + 2p = 108

l + m + p = 30

2l − m = 0

We form the augmented matrix for this system and row-reduce

From the row-reduced matrix, we see that we have an equivalent system l = 8, m = 16, and p = 6, which
means that you have 8 lizards, 16 mice and 6 peacocks.