Using a system of equations, it is found that:
- There are 8 chickens in the yard.
- There are 16 pigs in the yard.
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This question is solved using a system of equations. I am going to say that:
- x is the number of chickens.
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- A chicken has 1 head, as do a pig.
- There are 24 heads.
Thus:
![x + y = 24 \rightarrow y = 24 - x](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2024%20%5Crightarrow%20y%20%3D%2024%20-%20x)
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- A chicken has 2 feet.
- A pig has 4 feet.
- In total, there are 80 feet.
Thus:
![2x + 4y = 80](https://tex.z-dn.net/?f=2x%20%2B%204y%20%3D%2080)
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Number of chicken:
Since ![y = 24 - x](https://tex.z-dn.net/?f=y%20%3D%2024%20-%20x)
![2x + 4y = 80](https://tex.z-dn.net/?f=2x%20%2B%204y%20%3D%2080)
![2x + 4(24 - x) = 80](https://tex.z-dn.net/?f=2x%20%2B%204%2824%20-%20x%29%20%3D%2080)
![2x + 96 - 4x = 80](https://tex.z-dn.net/?f=2x%20%2B%2096%20-%204x%20%3D%2080)
![2x = 16](https://tex.z-dn.net/?f=2x%20%3D%2016)
![x = \frac{16}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B16%7D%7B2%7D)
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
There are 8 chickens in the yard.
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Number of pigs:
![y = 24 - x = 24 - 8 = 16](https://tex.z-dn.net/?f=y%20%3D%2024%20-%20x%20%3D%2024%20-%208%20%3D%2016)
There are 16 pigs in the yard.
A similar problem is given at brainly.com/question/24104709