A farmer had sheep and hens in his barnyard....there where a total of
40 heads and 100 feet.
How many hens and how many sheep did the farmer have?

You have 2 unknowns, so set up to 2 equations and solve simultaneously.

Keeping in mind that each sheep has 1 head, each hen 1 head, each
sheep has 4 feet, and each hen 2 feet

Let x = number of sheep
Let y = number of hens

Equation 1:  x + y = 40
This equation makes sense since there must be 40 heads

Equation 2: 4x + 2y = 100
This equation makes sense since each sheep has 4 feet and each hen has 2 feet.

Solve simultaneously:
x+y = 40
4x+2y = 100

You come up with x = # of sheep = 10
and y = # of chickens = 30

Just quickly, 10 Sheep and 30 chickens, 10 sheep = 40 legs, 30
chickens = 60 legs, 100 legs total, 40 heads.  I did this using excel.
 I've never been one for simultaneous equations I am afraid

Much simpler! No need for 2 variables.

Let number of sheep = x
Since there are 40 heads altogether
Number of hens = 40 - x

Sheep have 4 feet therfore total number of sheep feet = 4x
Hens have 2 feet therefore total number of hens feet = 2(40 - x)
Total feet 4x + 2(40 - x) = 100

ie 4x + 80 -2x = 100
       2x + 80 = 100
            2x = 20
             x = 10

ie number of sheep = 10 and number of hens = 40 - 10 = 30