A farmer has 38 animals only goats and chicken together they have116 legs how many of each type of animal are there?

g+c = 38 , -----> c = 38-g

4g+2c = 116

sub the first equation c = 38-g into the second equation
find g, then you can find c

To solve this problem, we can set up a system of equations based on the given information. Let's denote the number of goats as 'g' and the number of chickens as 'c'.

From the problem, we know that the total number of animals is 38, so we can write the equation:
g + c = 38 ---(Equation 1)

We also know that the total number of legs from goats and chickens combined is 116. Since each goat has 4 legs and each chicken has 2 legs, we can write the equation:
4g + 2c = 116 ---(Equation 2)

Now we have a system of equations consisting of Equation 1 and Equation 2. We can solve this system to find the values of 'g' and 'c'.

To eliminate one of the variables, we can multiply Equation 1 by 2, as it will make the coefficients of 'c' in both equations the same:

2g + 2c = 76 ---(Equation 3)

Now we can subtract Equation 3 from Equation 2 to eliminate 'c':

(4g + 2c) - (2g + 2c) = 116 - 76
2g = 40
g = 20

Substituting the value of 'g' into Equation 1, we can find the value of 'c':

20 + c = 38
c = 38 - 20
c = 18

So there are 20 goats and 18 chickens on the farm.