Question

A farmer has both pigs and chickens on his farm there are 78 fee and 27 heads how many pigs and how many chickens are there

Answer 1

Assuming health non-mutated animals:
$Feet = 4*Pigs + 2*Chickens$
$Heads = Pigs + Chickens$

By back substitution:
$78 = 4*(27-Chickens) + 2*Chickens$
$78 = 108 -2*Chickens$
$-30 = -2*Chickens$
$Chickens= 15$

Then:
$27 = Pigs + 15$
$Pigs = 12$

To check:
$Feet = 4*Pigs + 2*Chickens$
$78 = 4*12 + 2*15$
$78 = 48 + 30$
$78 = 78$ CHECKS