Question

a group of ducks and cows are in a field they have a total of 65 heads and 226 legs how many ducks are in the field

Answer 1

Each duck has 1 head and 2 legs. Each cow has 1 head and 4 legs.

Let x = number of ducks
y = number of cows

Then 1x + 1y = 65 ← heads
2x + 4y = 226 ← legs

Multiply the first equation by -2 and leave the second equation as is

-2x - 2y = -130
2x +4y = 226

Add the equations to obtain 2y = 96 So, y = 48
x = 17

There are 17 ducks and 48 cows.