There are 38 animals at a farm.some are cows some are chickens all together there are 124 legs . How many cows and how many chickens?

legs = 4 cows + 2 * chickens = 124

cows + chickens = 38
so
chickens = 38 - cows

4 cows + 2 (38 - cows) = 124

2 cows = 48

cows = 24
then
chickens = 14

To determine the number of cows and chickens at the farm, we need to use a system of equations. Let's assume the number of cows is 'C' and the number of chickens is 'Ch'.

We know that each cow has 4 legs and each chicken has 2 legs. There are a total of 38 animals at the farm, so we can create the equation:
C + Ch = 38 (Equation 1)

We also know that there are a total of 124 legs, so we can create the equation:
4C + 2Ch = 124 (Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (C and Ch).

We can solve these equations simultaneously to find the values of C and Ch using various methods such as substitution or elimination. Let's use the substitution method:

From Equation 1, we can express Ch in terms of C:
Ch = 38 - C

Now, substitute this value of Ch in Equation 2:
4C + 2(38 - C) = 124

Simplifying the equation:
4C + 76 - 2C = 124
2C + 76 = 124
2C = 124 - 76
2C = 48
C = 24

We have found that there are 24 cows at the farm.

Now, substitute this value of C back into Equation 1 to find the number of chickens:
24 + Ch = 38
Ch = 38 - 24
Ch = 14

We have found that there are 14 chickens at the farm.

Therefore, there are 24 cows and 14 chickens at the farm.