Answer:there are 11 goats and 17 ducks.
Step-by-step explanation:
Let x represent the number of goats in the field.
Let y represent the number of ducks in the field.
A farmer looks over a field and sees 28 heads and 78 feet. some are goats, some are ducks. A goat has one head and a duck also has one head. It means that
x + y = 28
A goat has 4 feets and a duck has two feets. It means that
4x + 2y = 78 - - - - - - - - - - - - - 1
Substituting x = 28 - y into equation 1, it becomes
4(28 - y) + 2y = 78
112 - 4y + 2y = 78
- 4y + 2y = 78 - 112
- 2y = - 34
y = - 34/- 2
y = 17
x = 28 - y = 28 - 17
x = 11
