Answer: the number of ducks in the field is 25
the number of pigs in the field is 9
Step-by-step explanation:
Let x represent the number of ducks in the field.
Let y represent the number of pigs in the field.
A duck has one head and a pig also has one head.
The number of ducks and pigs in a field totals 34. This means that
x + y = 34
The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, it means that
2x + 4y = 86 - - - - - - - - - - -- - 1
Substituting x = 34 - y into equation 1, it becomes
2(34 - y) + 4y = 86
68 - 2y + 4y = 86
- 2y + 4y = 86 - 68
2y = 18
y = 18/2 = 9
Substituting y = 9 into x = 34 - y, it becomes
x = 34 - 9 = 25
