Four loaves of bread and three packets of milk cost a total of Ksh. 410. Three similar loaves of bread and two similar packets of milk cost a total of Ksh. 290. Find the cost of one loaf of bread and the cost of one packet of milk.

Acha $b$ iwe gharama ya mkate mmoja na $m$ iwe gharama ya pakiti moja ya maziwa.
Kutokana na taarifa ya kwanza, tuna mlinganyo:

$$4b + 3m = 410 \quad \text{(Mlinganyo 1)}$$

Kutokana na taarifa ya pili, tuna mlinganyo:

$$3b + 2m = 290 \quad \text{(Mlinganyo 2)}$$

Ili kuondoa $m$, zidisha Mlinganyo 1 kwa 2 na Mlinganyo 2 kwa 3:
Zidisha Mlinganyo 1 kwa 2:

$$2(4b + 3m) = 2(410) \Rightarrow 8b + 6m = 820 \quad \text{(Mlinganyo 3)}$$

Zidisha Mlinganyo 2 kwa 3:

$$3(3b + 2m) = 3(290) \Rightarrow 9b + 6m = 870 \quad \text{(Mlinganyo 4)}$$

$$(9b + 6m) - (8b + 6m) = 870 - 820$$ $$9b - 8b + 6m - 6m = 50$$ $$b = 50$$

Hivyo, gharama ya mkate mmoja ni Sh. 50.

$$4b + 3m = 410$$ $$4(50) + 3m = 410$$ $$200 + 3m = 410$$ $$3m = 410 - 200$$ $$3m = 210$$ $$m = \frac{210}{3}$$ $$m = 70$$

Hivyo, gharama ya pakiti moja ya maziwa ni Sh. 70.

$$\text{Gharama ya mkate: Sh. 50, Gharama ya maziwa: Sh. 70}$$