A farmer buys 3 hens and 2 goats for sh 4500. Another farmer buys 3 hens and 5 goats for sh 9000. Find the cost of one hen and one goat.

Wacha $h$ iwe gharama ya kuku mmoja na $g$ iwe gharama ya mbuzi mmoja.
Kutoka taarifa ya kwanza:

$$3h + 2g = 4500 \quad \text{(Mlinganyo 1)}$$

Kutoka taarifa ya pili:

$$3h + 5g = 9000 \quad \text{(Mlinganyo 2)}$$

Ili kuondoa $h$, tutatoa Mlinganyo 1 kutoka Mlinganyo 2.

$$(3h + 5g) - (3h + 2g) = 9000 - 4500$$ $$3h + 5g - 3h - 2g = 4500$$ $$3g = 4500$$

Gawanya pande zote mbili kwa 3.

$$\frac{3g}{3} = \frac{4500}{3}$$ $$g = 1500$$

Tutatumia Mlinganyo 1 ($3h + 2g = 4500$).

$$3h + 2(1500) = 4500$$ $$3h + 3000 = 4500$$

Toa 3000 kutoka pande zote mbili.

$$3h = 4500 - 3000$$ $$3h = 1500$$

Gawanya pande zote mbili kwa 3.

$$\frac{3h}{3} = \frac{1500}{3}$$ $$h = 500$$

Gharama ya kuku mmoja ni Sh. 500 na gharama ya mbuzi mmoja ni Sh. 1500.

Gharama ya kuku mmoja ni: $\boxed{\text{Sh. } 500}$
Gharama ya mbuzi mmoja ni: $\boxed{\text{Sh. } 1500}$