Farmer John has goats and chickens on his farm. The total number of 4 legged goats and 2 legged chickens is 18. His son, Joseph counted 56 animal legs on the farm. Represent this situation with a system of linear equations and find the number of goats and chickens on the farm.

There are 10 (4-legged) goats and 8 (2-legged) chickens.

Step-by-step explanation:

Let x represent the number of 4 legged goats. Let y represent the number of 2 legged chickens.

The total number of 4 legged goats and 2 legged chickens is 18.

Therefore: x+y=18

His son, Joseph counted 56 animal legs on the farm.

The number of legs by x (4 legged) goats = 4x The number of legs by y (2 legged) Chickens = 2y

Therefore: 4x+2y=56

Solving the two equations simultaneously

x+y=18

4x+2y=56

From the first equation, x=18-y

Substitute x=18-y into the second equation

4x+2y=56

4 (18-y) + 2y=56

72-4y+2y=56

72-56=4y-2y

16=2y

y=8

Recall: x=18-y

x=18-8=10

x=10, y=8

There are 10 (4-legged) goats and 8 (2-legged) chickens.