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.
ScanSolve AI Answer
Ili kutatua milinganyo kwa njia ya grafu, tunahitaji kuchora mistari miwili inayowakilisha kila mlinganyo na kisha kupata sehemu wanapokutana. Milinganyo ni: 1) 3x - 2y = 5 2) 5x + y = 17 Step 1: Pata pointi mbili au zaidi kwa kila mlinganyo. Kwa mlinganyo wa kwanza, 3x - 2y = 5: Tengeneza y kuwa mada ya fomula: 2y = 3x - 5 y = (3x - 5)/(2) • Wakati x = 1: y = (3(1) - 5)/(2) = (-2)/(2) = -1. Pointi ni (1, -1). • Wakati x = 3: y = (3(3) - 5)/(2) = (9 - 5)/(2) = (4)/(2) = 2. Pointi ni (3, 2). • Wakati x = 5: y = (3(5) - 5)/(2) = (15 - 5)/(2) = (10)/(2) = 5. Pointi ni (5, 5). Kwa mlinganyo wa pili, 5x + y = 17: Tengeneza y kuwa mada ya fomula: y = 17 - 5x • Wakati x = 2: y = 17 - 5(2) = 17 - 10 = 7. Pointi ni (2, 7). • Wakati x = 3: y = 17 - 5(3) = 17 - 15 = 2. Pointi ni (3, 2). • Wakati x = 4: y = 17 - 5(4) = 17 - 20 = -3. Pointi ni (4, -3). Step 2: Chora grafu. Chora mfumo wa kuratibu wa Cartesian (x-axis na y-axis). • Panga pointi (1, -1), (3, 2), na (5, 5) kwa mlinganyo wa kwanza na chora mstari unaopita kati yake. • Panga pointi (2, 7), (3, 2), na (4, -3) kwa mlinganyo wa pili na chora mstari unaopita kati yake. Step 3: Tafuta sehemu ya makutano. Ukiangalia pointi tulizopata, utaona kwamba pointi (3, 2) inapatikana katika orodha zote mbili. Hii inamaanisha kuwa mistari miwili itakutana kwenye pointi hii. Suluhisho la milinganyo hii ni sehemu ya makutano ya mistari miwili, ambayo ni: x = 3, y = 2 Au kama jozi iliyopangwa: (3, 2) Got more? Send 'em!