a) Without using logarithm tables, find the value of x in the equation. b) Find the value of m in the following equation. c) Find the roots of the following equation using Factorization method.

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: $3x - 2y = 5$ $-2y = -3x + 5$ $y = \frac{3}{2}x - \frac{5}{2}$ $y = 1.5x - 2.5$

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 $s$. $s = \frac{-800}{-4}$ $s = 200$

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

\text{Sketi: Kshs 200, Blauzi: Kshs 250}

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