system of equations word problems

Question

There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in 

all. How many of each animal are there?

Answer 1

1) 2c+4p=40

2) c+p = 13 ⇒ c = 13-p

Take the first equation and place in it the value c=13-p

2(13-p)+4p=40

26-2p+4p=40

26+2p=40

2p=40-26

2p=14

p=7

Place the value p=7 into c=13-p ⇒ c=13-7 ⇒ c=6

∴ There are 6 chickens and 7 pigs.

Answer 2

C+P = 13

2C +4P = 40

C +2P =20

C +P = 13

P = 7 pigs

C = 6 chickesn