There are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside the cage. How many chickens are in there and how many rabbits?

Represent

r=number of rabbits

c=number of chickens

1 rabbit=4 feet and 1 head

1 chicen=2 feet and 1 head

rabbits head+chicen heads=72

1r+1c=72

feet=200

4 times r+2 times c=200

4r+2c=200

divide both sides by 2

2r+c=100

we have

r+c=72

2r+c=100

make first equation negative and add to second equation

-r-c=-72

2r+c=100 +

1r+0c=28

r=28

subsitute

r+c=72

28+c=72

subtract 28

c=44

44 chickens and 28 rabits