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 mfumo wa milinganyo kwa kutumia njia ya kubadilisha (substitution method), tutafuata hatua zifuatazo: Milinganyo iliyotolewa ni: 1) 2x + 5y = 38 2) 3x + 4y = 48 Step 1: Tenga kigezo kimoja kutoka kwa mlinganyo mmoja. Tutatenga x kutoka mlinganyo wa kwanza: 2x + 5y = 38 2x = 38 - 5y x = (38 - 5y)/(2) Step 2: Badilisha usemi huu wa x katika mlinganyo wa pili. 3((38 - 5y)/(2)) + 4y = 48 Step 3: Tatua mlinganyo unaotokana kwa y. Kuzidisha pande zote mbili za mlinganyo kwa 2 ili kuondoa sehemu: 2 · [3((38 - 5y)/(2)) + 4y] = 2 · 48 3(38 - 5y) + 8y = 96 114 - 15y + 8y = 96 114 - 7y = 96 -7y = 96 - 114 -7y = -18 y = (-18)/(-7) y = (18)/(7) Step 4: Badilisha thamani ya y uliyopata katika usemi wa x kutoka Hatua ya 1. x = (38 - 5(18)/(7))2 x = (38 - 90)/(7)2 Ili kurahisisha nambari, tunapata denominator ya kawaida: x = (38 × 7)/(7) - (90)/(7)2 x = (266)/(7) - (90)/(7)2 x = (266 - 90)/(7)2 x = (176)/(7)2 x = (176)/(7 × 2) x = (176)/(14) Rahisisha sehemu kwa kugawanya nambari na denominator kwa 2: x = (88)/(7) Kwa hiyo, suluhisho la mfumo wa milinganyo ni: x = (88)/(7), y = (18)/(7) That's 2 down. 3 left today — send the next one.