Answer:
The system of equation that represent this situations are;
![\left \{ {{h+s=15} \atop {0.2h+0.1s=2}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bh%2Bs%3D15%7D%20%5Catop%20%7B0.2h%2B0.1s%3D2%7D%7D%20%5Cright.)
Also 5 hats and 10 scarves can be prepared from 2 kg of yarn.
Step-by-step explanation:
Let number of hat Chevy makes be h.
Also Let number of scarves Chevy makes be s.
Given:
Total Amount of yarns = 2 kg
Total number of items = 15
Since Items need to make are hat and scarves.
Hence the equation can be represented as;
![h+s=15 \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=h%2Bs%3D15%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Again Given:
Each hat uses 0.2 kilograms of yarn.
each scarf uses 0.1 kilograms of yarn.
Hence the equation can be represented as;
![0.2h+0.1s=2 \ \ \ \ \ equation \ 2](https://tex.z-dn.net/?f=0.2h%2B0.1s%3D2%20%5C%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202)
Hence the system of equation that represent this situations are;
![\left \{ {{h+s=15} \atop {0.2h+0.1s=2}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bh%2Bs%3D15%7D%20%5Catop%20%7B0.2h%2B0.1s%3D2%7D%7D%20%5Cright.)
Now Solving these to find number of hats and number of scarves.
Multiplying equation 2 with 10 we get;
![10(0.2h+0.1s)=2\times 10\\10\times0.2h+10\times0.1s=20\\2h+s =20 \ \ \ \ \ equation \ 3](https://tex.z-dn.net/?f=10%280.2h%2B0.1s%29%3D2%5Ctimes%2010%5C%5C10%5Ctimes0.2h%2B10%5Ctimes0.1s%3D20%5C%5C2h%2Bs%20%3D20%20%5C%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%203)
Now Subtracting equation 1 from equation 3 we get;
![(2h+s)- (h+s) =20-15\\2h+s-h-s=5\\h= 5](https://tex.z-dn.net/?f=%282h%2Bs%29-%20%28h%2Bs%29%20%3D20-15%5C%5C2h%2Bs-h-s%3D5%5C%5Ch%3D%205)
Now Substituting the value of h in equation 1 we get;
![h+s= 15\\5+s =15\\s=15-5\\s=10](https://tex.z-dn.net/?f=h%2Bs%3D%2015%5C%5C5%2Bs%20%3D15%5C%5Cs%3D15-5%5C%5Cs%3D10)
Hence 5 hats and 10 scarves can be prepared from 2 kg of yarn.