Answer:
There are 14 rabbits and 21 pheasants in the yard.
Step-by-step explanation:
Since we don't know the number of animals, lets introduce two variables: the number of rabbits are x and the number of pheasants are y.
Rabbits have 4 feet, so the equation to find the total feet of all rabbit would be 4x.
Pheasants have 2 feet, so the equation to find all of their feet would be 2y.
The total number of heads is 35. Since there are x rabbits and y pheasants, and all of them have 1 head, we get this:
[tex]x + y = 35[/tex]
The total number of legs is 98. Since all rabbits have a total of 4x legs and all pheasants have 2y legs, we get this:
[tex]4x + 2y = 98[/tex]
If we use them together, we get a linear equation, which we can solve for x:
[tex]x + y = 35 \: \: ( \times - 2)\\ 4x + 2y = 98[/tex]
[tex] \: \: \: \: \: \: - 2x - 2y = - 70 \\ + \: \: \: \: \: \: 4x + 2y = 98[/tex]
[tex]2x = 28 \\ x = 14[/tex]
So, there are 14 rabbits. We can find the number of pheasants by diving 14 heads from the total of 35 heads:
[tex]35 - 14 = y \\ y = 21[/tex]
and so we have 21 pheasants.
