Old mcdonald has some chickens and some cows. he counted 56 heads and 116 legs. how many chickens and how many cows does old mcdonald have? (the animals are not missing any legs or head's)

old McDonald has 54 chickens and 2 cows.

Step-by-step explanation:

Let x represent the number of chickens that old McDonald have.

Let y represent the number of cows that old McDonald have.

He counted 56 heads. A chicken and a cow has one head each. It means that

x + y = 56

He counted 116 legs. A chicken has 2 legs and a cow has 4 legs. It means that

2x + 4y = 116 - - - - - - - - -1

Substituting x = 56 - y into equation 1, it becomes

2(56 - y) + 4y = 116

112 - 2y + 4y = 116

- 2y + 4y = 116 - 112

2y = 4

y = 4/2 = 2

x = 56 - y = 56 - 2

x = 54

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

k

step-by-step explanation:

domit