The two Hens & Rabbits applets represent the same problem in two different ways.
A farmer has 50 animals. Some are hens & some are rabbits. Among them they have a total of 140 legs. How many hens and how many rabbits does the farmer have?
[answer 30 hens, 20 rabbits]
One graphical representation of the problem shows the problem in the {animals, feet} plane and the other graphical representation shows the problem in the {hens, rabbits} plane.
Study the two representations carefully -
How are the numbers of rabbits and the number of hens represented in the {animals, feet} plane?
How are the number of animals and the number of feet represented in the {hens, rabbits} plane?
How are the quantities feet/rabbit and feet/hen represented in each of the two planes?
Which representation do you think provides you with more insight? Why?