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

C=chicken
p=pigs
c+p=13~p=13-c (plug in)
2c+4p=40
2c+4(13-c)=40
2c+52-4c=40
-2c=-12
c=6
6+p=13
p=7
6 chickens
7 pigs

Answer 2

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