This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Sawa Roy, hebu tusuluhishe swali la 17. 17 a) Tatua kielelezo milinganyo shirikishi 3x - 2y = 5 na 5x + y = 17. Step 1: Andika upya kila mlinganyo katika mfumo wa y = mx + c ili kurahisisha kuchora grafu. Kwa mlinganyo wa kwanza: 3x - 2y = 5 -2y = -3x + 5 y = (3)/(2)x - (5)/(2) y = 1.5x - 2.5 Kwa mlinganyo wa pili: 5x + y = 17 y = -5x + 17 Step 2: Pata pointi mbili au tatu kwa kila mstari ili kuchora grafu. Kwa y = 1.5x - 2.5: • Ikiwa x = 0, y = 1.5(0) - 2.5 = -2.5. Pointi ni (0, -2.5). • Ikiwa x = 2, y = 1.5(2) - 2.5 = 3 - 2.5 = 0.5. Pointi ni (2, 0.5). • Ikiwa x = 4, y = 1.5(4) - 2.5 = 6 - 2.5 = 3.5. Pointi ni (4, 3.5). Kwa y = -5x + 17: • Ikiwa x = 0, y = -5(0) + 17 = 17. Pointi ni (0, 17). • Ikiwa x = 2, y = -5(2) + 17 = -10 + 17 = 7. Pointi ni (2, 7). • Ikiwa x = 3, y = -5(3) + 17 = -15 + 17 = 2. Pointi ni (3, 2). Step 3: Chora mistari kwenye grafu. Chora mhimili wa x na mhimili wa y. Panga pointi ulizopata kwa kila mlinganyo na kisha chora mstari unaopita kwenye pointi hizo. Step 4: Tambua sehemu ya makutano. Sehemu ambayo mistari miwili inakutana ndiyo suluhisho la milinganyo shirikishi. Kutoka kwenye pointi zetu, tunaona kwamba pointi (3, 2) inapatikana kwenye mistari yote miwili. Hivyo, x = 3 na y = 2. Suluhisho la kielelezo ni: x = 3, y = 2 x = 3, y = 2 17 b) Gharama ya sketi 5 na blauzi 3 ni Kshs 1750. Mueni alinunua sketi tatu na blauzi moja kwa Kshs 850. Tafuta gharama ya kila bidhaa. Step 1: Unda milinganyo shirikishi. Acha s iwe gharama ya sketi moja na b iwe gharama ya blauzi moja. Kutoka taarifa ya kwanza: "Gharama ya sketi 5 na blauzi 3 ni Kshs 1750." Mlinganyo 1: 5s + 3b = 1750 Kutoka taarifa ya pili: "Mueni alinunua sketi tatu na blauzi moja kwa Kshs 850." Mlinganyo 2: 3s + b = 850 Step 2: Tatua milinganyo shirikishi. Kutoka Mlinganyo 2, tunaweza kutoa b: b = 850 - 3s Step 3: Badilisha thamani ya b katika Mlinganyo 1. 5s + 3(850 - 3s) = 1750 5s + 2550 - 9s = 1750 -4s = 1750 - 2550 -4s = -800 Step 4: Tafuta thamani ya s. s = (-800)/(-4) s = 200 Step 5: Tafuta thamani ya b kwa kutumia thamani ya s. b = 850 - 3s b = 850 - 3(200) b = 850 - 600 b = 250 Hivyo, gharama ya sketi moja ni Kshs 200 na gharama ya blauzi moja ni Kshs 250. Gharama ya sketi: Kshs 200 Gharama ya blauzi: Kshs 250 Sketi: Kshs 200, Blauzi: Kshs 250 That's 2 down. 3 left today — send the next one.