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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Ili kuchora grafu ya milinganyo hii, tunahitaji kupata pointi mbili au zaidi kwa kila mlinganyo, kisha tuchore mstari unaopita kwenye pointi hizo. a) x + y = 4 Step 1: Tafuta pointi mbili. Ili kurahisisha, tunaweza kuweka x=0 ili kupata y, na kisha kuweka y=0 ili kupata x. Kama x = 0: 0 + y = 4 y = 4 Hivyo, pointi ya kwanza ni (0, 4). Kama y = 0: x + 0 = 4 x = 4 Hivyo, pointi ya pili ni (4, 0). Step 2: Chora grafu. Chora mfumo wa kuratibu wa x-y. Weka alama kwenye pointi (0, 4) na (4, 0). Kisha, chora mstari ulionyooka unaopita kwenye pointi hizi mbili. Huu ndio uwakilishi wa grafu wa mlinganyo x + y = 4. b) 2y + x = -7 Step 1: Tafuta pointi mbili. Kama x = 0: 2y + 0 = -7 2y = -7 y = -(7)/(2) = -3.5 Hivyo, pointi ya kwanza ni (0, -3.5). Kama y = 0: 2(0) + x = -7 x = -7 Hivyo, pointi ya pili ni (-7, 0). Step 2: Chora grafu. Chora mfumo wa kuratibu wa x-y. Weka alama kwenye pointi (0, -3.5) na (-7, 0). Kisha, chora mstari ulionyooka unaopita kwenye pointi hizi mbili. Huu ndio uwakilishi wa grafu wa mlinganyo 2y + x = -7. c) 8 - x = 4 - x Step 1: Rahisisha mlinganyo. 8 - x = 4 - x Ongeza x pande zote mbili za mlinganyo: 8 - x + x = 4 - x + x 8 = 4 Step 2: Tafsiri matokeo. Mlinganyo 8 = 4 ni kauli ya uongo. Hii inamaanisha kuwa hakuna thamani ya x inayoweza kufanya mlinganyo huu kuwa kweli. Kwa hivyo, mlinganyo huu hauna suluhisho na hauwezi kuwakilishwa na grafu kwenye mfumo wa kuratibu wa x-y. Send me the next one 📸