Alex and Sharmim went to a supermarket to buy books and pens. Alex bought 3 books and 2 pens and paid sh 190. Sharmim bought 4 books and 7 pens and paid sh 340. Determine the selling price of a book and that of a pen by using the graphical method.

Acha $x$ iwe bei ya kitabu kimoja na $y$ iwe bei ya kalamu moja.
Kutokana na ununuzi wa Alex, tuna mlinganyo:

Kutokana na ununuzi wa Sharmim, tuna mlinganyo:

Kwa Mlinganyo 1 ($3x + 2y = 190$):

• Chagua $x = 0$: $3(0) + 2y = 190 \Rightarrow 2y = 190 \Rightarrow y = 95$. Pointi ni $(0, 95)$.
• Chagua $x = 50$: $3(50) + 2y = 190 \Rightarrow 150 + 2y = 190 \Rightarrow 2y = 40 \Rightarrow y = 20$. Pointi ni $(50, 20)$.

Kwa Mlinganyo 2 ($4x + 7y = 340$):

• Chagua $x = 0$: $4(0) + 7y = 340 \Rightarrow 7y = 340 \Rightarrow y \approx 48.57$. Pointi ni $(0, 48.57)$.
• Chagua $x = 50$: $4(50) + 7y = 340 \Rightarrow 200 + 7y = 340 \Rightarrow 7y = 140 \Rightarrow y = 20$. Pointi ni $(50, 20)$.

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 $(50, 20)$ ipo kwenye mistari yote miwili. Hivyo, sehemu ya makutano ni $(50, 20)$.

Thamani ya $x$ kwenye sehemu ya makutano inawakilisha bei ya kitabu, na thamani ya $y$ inawakilisha bei ya kalamu.
Bei ya kitabu kimoja ni sh. 50.
Bei ya kalamu moja ni sh. 20.