There are 42 animals in a farmyard. some are cows and some are chickens. in total there are 104 legs. how many chickens are there?

Cows(m) have 4 legs, chickens(c) have 2. Setting up a system of equations 104=4m+2c and 42=m+c. Solved for c the latter equation becomes 42-m=c. Using substitution in the first equation 104=4m+2(42-m). Distribute: 104=4m+84-2m. Combine like terms: 104=2m+84. Isolate variable term: 104-84=2m. Variable coefficient 1: 20/2=10=m. 42-10=32=c.   10 cows and 32 chickens.