Let x = number of chickens

Let y = number of sheep

Then x + y = 36

Chickens have 2 legs each, sheep have 4 legs each, and there are 82 legs altogether.

So: 2x + 4y = 82

We now have 2 simultaneous equations:

x + y = 36 (Equation 1)

2x + 4y = 82 (Equation 2)

Equation 1 multiplied by 2 gives:

2x + 2y = 72 (Equation 3)

Subtracting equation 3 from equation 2 gives:

2y = 10

So y = 5.

Substituting y = 5 into equation 1 (it doesn't really matter which equation you substitute in) gives:

x + (5) = 36

So x = 31