There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

Step 1 ：Let's denote the number of chickens as x and the number of pigs as y. We know that chickens have 2 legs and pigs have 4 legs.

Step 2 ：We can set up the following equations based on the problem: \(x + y = 13\) (total number of animals) and \(2x + 4y = 40\) (total number of legs).

Step 3 ：We can solve this system of equations to find the values of x and y.

Step 4 ：The solution to the system of equations is \(x = 6\) and \(y = 7\).

Step 5 ：Final Answer: There are \(\boxed{6}\) chickens and \(\boxed{7}\) pigs in the barn.