Camila bought 5 cups and 8 plates and paid sh 1050 while her friend Linnet bought 4 cups and 10 plates from the same shop and sh 1200. Use graphical method to determine the cost of a cup and that of a plate.

Acha $x$ iwe bei ya kikombe kimoja na $y$ iwe bei ya sahani moja.
Kutokana na ununuzi wa Camila, tuna mlinganyo:

Kutokana na ununuzi wa Linet, tuna mlinganyo:

Kwa Mlinganyo 1 ($5x + 8y = 1050$):

• Chagua $x = 0$: $5(0) + 8y = 1050 \Rightarrow 8y = 1050 \Rightarrow y = 131.25$. Pointi ni $(0, 131.25)$.
• Chagua $x = 50$: $5(50) + 8y = 1050 \Rightarrow 250 + 8y = 1050 \Rightarrow 8y = 800 \Rightarrow y = 100$. Pointi ni $(50, 100)$.
• Chagua $y = 0$: $5x + 8(0) = 1050 \Rightarrow 5x = 1050 \Rightarrow x = 210$. Pointi ni $(210, 0)$.

Jedwali la Mlinganyo 1:

Kwa Mlinganyo 2 ($4x + 10y = 1200$):

• Chagua $x = 0$: $4(0) + 10y = 1200 \Rightarrow 10y = 1200 \Rightarrow y = 120$. Pointi ni $(0, 120)$.
• Chagua $x = 50$: $4(50) + 10y = 1200 \Rightarrow 200 + 10y = 1200 \Rightarrow 10y = 1000 \Rightarrow y = 100$. Pointi ni $(50, 100)$.
• Chagua $y = 0$: $4x + 10(0) = 1200 \Rightarrow 4x = 1200 \Rightarrow x = 300$. Pointi ni $(300, 0)$.

Jedwali la Mlinganyo 2:

Chora mfumo wa kuratibu (x-axis na y-axis). Panga pointi ulizopata kwa Mlinganyo 1 na chora mstari unaounganisha pointi hizo. Kisha, panga pointi ulizopata kwa Mlinganyo 2 na chora mstari unaounganisha pointi hizo.

Sehemu ambapo mistari miwili inakutana ndio suluhisho la milinganyo. Kutoka kwa pointi tulizopata, tunaona kwamba pointi $(50, 100)$ ipo kwenye mistari yote miwili. Hivyo, sehemu ya makutano ni $(50, 100)$.

Thamani ya $x$ kwenye sehemu ya makutano inawakilisha bei ya kikombe, na thamani ya $y$ inawakilisha bei ya sahani.
Bei ya kikombe kimoja ni Sh. 50.
Bei ya sahani moja ni Sh. 100.