There are 13 animals in a barn. some are ducks and some are pigs. there are 40 legs in all. how many of each animal are there?

Let X be chickens

Let Y be pigs,

then x+y=13

the animals have 2x+4y legs,

so 2x+4y=40

The system of the equations

[X+y=13

[2x+4y=40

Divide the second equation by 2

[x+y=13

[x+2y=20

subtract the first equation from the second one

y=20-13

y-7 pigs

substitute y=7 into the first equation

x+7=13

x=13-7

x=6 chickens