In a pen with rabbits and chickens someone counted 25 heads and 80 legs a rabbit has four legs and each chicken has 2 legs, how many chickens and rabbits are there?

I just kind of sat here playing with numbers i dont really know a shortcut but the answer is 10 chickens and 15 rabbits 
10*2= 20 each chicken has two legs so thats 10 heads 20 legs
15*4=60 each rabbit has four legs so thats 15 heads 60 legs
15+10=25 heads
20+60=60 legs

Let "rabbits" be represented by the variable "x"
and "chickens" be represented by the variable "y"

then in total we have 25 animals
so  x + y = 25
-> y = -x + 25
and since a rabbit has four legs and a chicken has two legs
and there are 80 legs in total
4x + 2y = 80
-> 2x + y = 40
-> y = -2x + 40

[I had solved for y for each equation]
and since we are looking for when  y = y
-x + 25 = -2x + 40   [we can solve for x from here]
x + 25 = 40     [added 2x to both sides]
x = 15  [subtracted 25 from both sides]

then we can plug this back into
y = -x + 25
to get  y = -15 + 25 = 10

therefore there are 15 Rabbits and 10 Chickens

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