System of Linear Equations Algerba Book A Word Problem Question

Question

An algebra teacher drove by a farmyard full of chickens and pigs. The teacher happened to notice that there were a total of 100 heads and 270 legs. How mnay chickens were there? How many pigs were there?

 

I need the answer to be in the form of a plot point.

For example: (-2,-2), or (72,28)

Answer 1

Each chicken and pig has one head. Chickens have two legs each and pigs have 4 each.

So if c=number of chickens and p=number of pigs:

c+p=100 and 2c+4p=270, that is, c+2p=135.

c=100-p=135-2p, therefore 100-p=135-2p, 2p-p=135-100, p=35. So there are 35 pigs and 100-35=65 chickens. This can be written (c,p)=(65,35).