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.

Step 1: Fafanua vigezo na uandike milinganyo. Acha x iwe bei ya kikombe kimoja na y iwe bei ya sahani moja. Kutokana na ununuzi wa Camila, tuna mlinganyo: 5x + 8y = 1050 (Mlinganyo 1) Kutokana na ununuzi wa Linet, tuna mlinganyo: 4x + 10y = 1200 (Mlinganyo 2) Step 2: Tafuta pointi mbili au zaidi kwa kila mlinganyo ili kuchora mistari. Kwa Mlinganyo 1 (5x + 8y = 1050): • Chagua x = 0: 5(0) + 8y = 1050 8y = 1050 y = 131.25. Pointi ni (0, 131.25). • Chagua x = 50: 5(50) + 8y = 1050 250 + 8y = 1050 8y = 800 y = 100. Pointi ni (50, 100). • Chagua y = 0: 5x + 8(0) = 1050 5x = 1050 x = 210. Pointi ni (210, 0). Jedwali la Mlinganyo 1: | x | y | |-----|-----| | 0 | 131.25 | | 50 | 100 | | 210 | 0 | Kwa Mlinganyo 2 (4x + 10y = 1200): • Chagua x = 0: 4(0) + 10y = 1200 10y = 1200 y = 120. Pointi ni (0, 120). • Chagua x = 50: 4(50) + 10y = 1200 200 + 10y = 1200 10y = 1000 y = 100. Pointi ni (50, 100). • Chagua y = 0: 4x + 10(0) = 1200 4x = 1200 x = 300. Pointi ni (300, 0). Jedwali la Mlinganyo 2: | x | y | |-----|-----| | 0 | 120 | | 50 | 100 | | 300 | 0 | Step 3: Chora grafu. 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. Step 4: Tafuta sehemu ya makutano. 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). Step 5: Andika jibu. 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. Bei ya kikombe: Sh. 50, Bei ya sahani: Sh. 100 That's 2 down. 3 left today — send the next one.