let p = pigs
and c = chickens
p + c = 13 ( this is the total number of animals in the barn)
chicken have 2 legs and pigs have 4 legs
2c + 4p = 40 ( this is the equation for the total number of legs)
now lets solve for one variable using the first equation
p+c = 13
p = 13 -c
now lets plug that in the 2nd equation
2c+4p = 40
2c + 4(13-c) = 40
2c + 52 - 4c = 40
now we reduce
-2c = -12
c = 6
so there are 6 chickens now lets find how many pigs there are by plugging into our first equation
p+6 = 13
p = 7
so there are 6 chickens and 7 pigs
