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
Haya man, tutatatua milinganyo hii kwa kutumia njia ya grafu. Milinganyo uliyopewa ni: 1. 3x - 2y = 5 2. 5x + y = 17 Step 1: Panga upya milinganyo ili y iwe mada. Hii itarahisisha kupata pointi za kuchora. Kwa mlinganyo wa kwanza (3x - 2y = 5): -2y = 5 - 3x 2y = 3x - 5 y = (3x - 5)/(2) Kwa mlinganyo wa pili (5x + y = 17): y = 17 - 5x Step 2: Tafuta pointi mbili au zaidi kwa kila mstari. Tutachagua thamani za x na kuhesabu thamani zinazolingana za y. Kwa mstari wa kwanza (y = (3x - 5)/(2)): • Chagua x=1: y = (3(1) - 5)/(2) = (3 - 5)/(2) = (-2)/(2) = -1 Pointi ya kwanza ni (1, -1). • Chagua x=3: y = (3(3) - 5)/(2) = (9 - 5)/(2) = (4)/(2) = 2 Pointi ya pili ni (3, 2). Kwa mstari wa pili (y = 17 - 5x): • Chagua x=2: y = 17 - 5(2) = 17 - 10 = 7 Pointi ya kwanza ni (2, 7). • Chagua x=3: y = 17 - 5(3) = 17 - 15 = 2 Pointi ya pili ni (3, 2). Step 3: Chora mistari kwenye grafu. Chora pointi hizi kwenye karatasi ya grafu. Kisha, chora mstari ulionyooka kupitia pointi za kila mlinganyo. • Kwa 3x - 2y = 5, chora mstari unaopitia (1, -1) na (3, 2). • Kwa 5x + y = 17, chora mstari unaopitia (2, 7) na (3, 2). Step 4: Tafuta sehemu ya makutano. Sehemu ambayo mistari miwili inakutana ndiyo suluhisho la milinganyo. Kutoka kwa pointi tulizopata, tunaona kwamba pointi (3, 2) ipo kwenye mistari yote miwili. Hii inamaanisha kwamba mistari inakutana kwenye pointi hiyo. Hivyo, suluhisho la milinganyo hii ni: x = 3 na y = 2. x=3, y=2 That's 2 down. 3 left today — send the next one.