have 4 legs and all the chickens have 2 legs.
A farm has chickens and cows. All the cows have 4 legs and all the chicke
All together, there are 82 cow and chicken legs on the farm. Complete the table to
show some possible combinations of chickens and cows to get 82 total legs.
number of chickens (x)
number of cows (y)
35
10
19
7

A farm has chickens and cows. All the cows have 4 legs and all the chickens have 2 legs. All together, there are 82 cow and chicken legs on the farm. Complete the table to show some possible combinations of chickens and cows to get 82 total legs.

Let

x ----> number of chickens

y ----> number of cows

we know that

The number of chickens multiplied by 2 plus the number of cows multiplied by 4 must be equal to 82

Remember that the values of x and y must be whole numbers

The linear equation that represent this situation is

[tex]2x+4y=82[/tex]

Solve for y

That means----> Isolate the variable y

[tex]4y=-2x+82[/tex]

[tex]y=-0.5x+20.5[/tex]

Complete the table

For [tex]x=7\ chickens[/tex] ---> [tex]y=-0.5(7)+20.5=17\ cows[/tex]

For [tex]x=19\ chickens[/tex] ---> [tex]y=-0.5(19)+20.5=11\ cows[/tex]

For [tex]y=10\ cows[/tex]

[tex]2x+4(10)=82[/tex]

[tex]2x=82-40[/tex]

[tex]2x=42[/tex]

[tex]x=21\ chickens[/tex]

For [tex]x=35\ chickens[/tex] ---> [tex]y=-0.5(35)+20.5=3\ cows[/tex]