5.2E: Mazoezi
- Page ID
- 177344
Mazoezi hufanya kamili
Tatua Mfumo wa Ulinganisho kwa Kubadilisha
Katika mazoezi yafuatayo, tatua mifumo ya equations kwa kubadilisha.
\(\left\{\begin{array}{l}{2 x+y=-4} \\ {3 x-2 y=-6}\end{array}\right.\)
- Jibu
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\((−2,0)\)
\(\left\{\begin{array}{l}{2 x+y=-2} \\ {3 x-y=7}\end{array}\right.\)
\(\left\{\begin{array}{l}{x-2 y=-5} \\ {2 x-3 y=-4}\end{array}\right.\)
- Jibu
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\((7,6)\)
\(\left\{\begin{array}{l}{x-3 y=-9} \\ {2 x+5 y=4}\end{array}\right.\)
\(\left\{\begin{array}{l}{5 x-2 y=-6} \\ {y=3 x+3}\end{array}\right.\)
- Jibu
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\((0,3)\)
\(\left\{\begin{array}{l}{-2 x+2 y=6} \\ {y=-3 x+1}\end{array}\right.\)
\(\left\{\begin{array}{l}{2 x+3 y=3} \\ {y=-x+3}\end{array}\right.\)
- Jibu
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\((6,−3)\)
\(\left\{\begin{array}{l}{2 x+5 y=-14} \\ {y=-2 x+2}\end{array}\right.\)
\(\left\{\begin{array}{l}{2 x+5 y=1} \\ {y=\frac{1}{3} x-2}\end{array}\right.\)
- Jibu
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\((3,−1)\)
\(\left\{\begin{array}{l}{3 x+4 y=1} \\ {y=-\frac{2}{5} x+2}\end{array}\right.\)
\(\left\{\begin{array}{l}{3 x-2 y=6} \\ {y=\frac{2}{3} x+2}\end{array}\right.\)
- Jibu
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\((6,6)\)
\(\left\{\begin{array}{l}{-3 x-5 y=3} \\ {y=\frac{1}{2} x-5}\end{array}\right.\)
\(\left\{\begin{array}{l}{2 x+y=10} \\ {-x+y=-5}\end{array}\right.\)
- Jibu
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\((5,0)\)
\(\left\{\begin{array}{l}{-2 x+y=10} \\ {-x+2 y=16}\end{array}\right.\)
\(\left\{\begin{array}{l}{3 x+y=1} \\ {-4 x+y=15}\end{array}\right.\)
- Jibu
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\((−2,7)\)
\(\left\{\begin{array}{l}{x+y=0} \\ {2 x+3 y=-4}\end{array}\right.\)
\(\left\{\begin{array}{l}{x+3 y=1} \\ {3 x+5 y=-5}\end{array}\right.\)
- Jibu
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\((−5,2)\)
\(\left\{\begin{array}{l}{x+2 y=-1} \\ {2 x+3 y=1}\end{array}\right.\)
\(\left\{\begin{array}{l}{2 x+y=5} \\ {x-2 y=-15}\end{array}\right.\)
- Jibu
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\((−1,7)\)
\(\left\{\begin{array}{l}{4 x+y=10} \\ {x-2 y=-20}\end{array}\right.\)
\(\left\{\begin{array}{l}{y=-2 x-1} \\ {y=-\frac{1}{3} x+4}\end{array}\right.\)
- Jibu
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\((−3,5)\)
\(\left\{\begin{array}{l}{y=x-6} \\ {y=-\frac{3}{2} x+4}\end{array}\right.\)
\(\left\{\begin{array}{l}{y=2 x-8} \\ {y=\frac{3}{5} x+6}\end{array}\right.\)
- Jibu
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\((10, 12)\)
\(\left\{\begin{array}{l}{y=-x-1} \\ {y=x+7}\end{array}\right.\)
\(\left\{\begin{array}{l}{4 x+2 y=8} \\ {8 x-y=1}\end{array}\right.\)
- Jibu
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\(\left(\frac{1}{2}, 3\right)\)
\(\left\{\begin{array}{l}{-x-12 y=-1} \\ {2 x-8 y=-6}\end{array}\right.\)
\(\left\{\begin{array}{l}{15 x+2 y=6} \\ {-5 x+2 y=-4}\end{array}\right.\)
- Jibu
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\(\left(\frac{1}{2},-\frac{3}{4}\right)\)
\(\left\{\begin{array}{l}{2 x-15 y=7} \\ {12 x+2 y=-4}\end{array}\right.\)
\(\left\{\begin{array}{l}{y=3 x} \\ {6 x-2 y=0}\end{array}\right.\)
- Jibu
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Ufumbuzi mkubwa sana. Equations mbili zinawakilisha mstari huo.
Suluhisho lililowekwa ni: Pointi\(\big\{ (x,y)\, | \,y = 3 x \big\}\)
zote ambazo ni ufumbuzi wa equation\(y=3x\) ni ufumbuzi wa mfumo huu.
\(\left\{\begin{array}{l}{x=2 y} \\ {4 x-8 y=0}\end{array}\right.\)
\(\left\{\begin{array}{l}{2 x+16 y=8} \\ {-x-8 y=-4}\end{array}\right.\)
- Jibu
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Ufumbuzi mkubwa sana. Equations mbili zinawakilisha mstari huo.
Suluhisho lililowekwa ni: Pointi\(\big\{ (x,y) \,| \,2 x +16 y = 8 \big\}\)
zote ambazo ni ufumbuzi wa equation\(2 x +16 y = 8 \) ni ufumbuzi wa mfumo huu.
\(\left\{\begin{array}{l}{15 x+4 y=6} \\ {-30 x-8 y=-12}\end{array}\right.\)
\(\left\{\begin{array}{l}{y=-4 x} \\ {4 x+y=1}\end{array}\right.\)
- Jibu
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Hakuna ufumbuzi
\(\left\{\begin{array}{l}{y=-\frac{1}{4} x} \\ {x+4 y=8}\end{array}\right.\)
\(\left\{\begin{array}{l}{y=\frac{7}{8} x+4} \\ {-7 x+8 y=6}\end{array}\right.\)
- Jibu
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Hakuna ufumbuzi
\(\left\{\begin{array}{l}{y=-\frac{2}{3} x+5} \\ {2 x+3 y=11}\end{array}\right.\)
Tatua Matumizi ya Mifumo ya Ulinganisho na Kubadilisha
Katika mazoezi yafuatayo, tafsiri kwa mfumo wa equations na kutatua.
Jumla ya namba mbili ni 15. Nambari moja ni 3 chini ya nyingine. Kupata idadi.
- Jibu
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Idadi ni 6 na 9.
Jumla ya namba mbili ni 30. Nambari moja ni 4 chini ya nyingine. Kupata idadi.
Jumla ya namba mbili ni -26. Nambari moja ni chini ya 12 kuliko nyingine. Kupata idadi.
- Jibu
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Nambari ni -7 na -19.
Mzunguko wa mstatili ni 50. Urefu ni 5 zaidi ya upana. Pata urefu na upana.
Mzunguko wa mstatili ni 60. Urefu ni 10 zaidi ya upana. Pata urefu na upana.
- Jibu
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Urefu ni 20 na upana ni 10.
Mzunguko wa mstatili ni 58. Urefu ni 5 zaidi ya mara tatu upana. Pata urefu na upana.
Mzunguko wa mstatili ni 84. Urefu ni 10 zaidi ya mara tatu upana. Pata urefu na upana.
- Jibu
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Urefu ni 34 na upana ni 8.
Kipimo cha moja ya pembe ndogo za pembetatu ya kulia ni 14 zaidi ya mara 3 kipimo cha angle nyingine ndogo. Pata kipimo cha pembe zote mbili.
Kipimo cha moja ya pembe ndogo za pembetatu ya kulia ni 26 zaidi ya mara 3 kipimo cha angle nyingine ndogo. Pata kipimo cha pembe zote mbili.
- Jibu
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\(\text { The measures are } 16^{\circ} \text { and } 74^{\circ}\)
Kipimo cha moja ya pembe ndogo za pembetatu ya kulia ni 15 chini ya mara mbili kipimo cha angle nyingine ndogo. Pata kipimo cha pembe zote mbili.
Kipimo cha moja ya pembe ndogo za pembetatu ya kulia ni 45 chini ya mara mbili kipimo cha angle nyingine ndogo. Pata kipimo cha pembe zote mbili.
- Jibu
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Hatua ni\(45^{\circ}\) na\(45^{\circ} .\)
Maxim imekuwa inayotolewa nafasi na wafanyabiashara wawili gari. Kampuni ya kwanza inalipa mshahara wa dola 10,000 pamoja na tume ya $1,000 kwa kila gari lililouzwa. Ya pili hulipa mshahara wa $20,000 pamoja na tume ya $500 kwa kila gari lililouzwa. Ni magari ngapi yangehitaji kuuzwa ili kulipa jumla sawa?
Jackie amepewa nafasi na makampuni mawili ya cable. Kampuni ya kwanza inalipa mshahara wa $14,000 pamoja na tume ya $100 kwa kila mfuko wa cable unauzwa. Ya pili hulipa mshahara wa $20,000 pamoja na tume ya $25 kwa kila mfuko wa cable kuuzwa. Ni vifurushi ngapi vya cable vinavyohitajika kuuzwa ili kulipa jumla sawa?
- Jibu
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80 paket cable bila haja ya kuuzwa.
Amara kwa sasa anauza televisheni kwa kampuni A kwa mshahara wa $17,000 pamoja na tume ya $100 kwa kila televisheni anayouza. Kampuni B inampa nafasi na mshahara wa $29,000 pamoja na tume ya $20 kwa kila televisheni anayouza. Jinsi gani televisheni Amara ingehitaji kuuza ili chaguzi ziwe sawa?
Mitchell kwa sasa anauza majiko kwa kampuni A kwa mshahara wa $12,000 pamoja na tume ya $150 kwa kila jiko anayouza. Kampuni B inampa nafasi na mshahara wa $24,000 pamoja na tume ya $50 kwa kila jiko anazouza. Ngapi jiko itakuwa Mitchell haja ya kuuza kwa ajili ya chaguzi kuwa sawa?
- Jibu
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Mitchell bila haja ya kuuza majiko 120.
kila siku Math
Wakati Gloria alitumia dakika 15 kwenye mkufunzi wa elliptical na kisha alifanya mafunzo ya mzunguko kwa dakika 30, programu yake ya fitness inasema alichomwa kalori 435. Alipotumia dakika 30 kwenye mkufunzi wa elliptical na mafunzo ya mzunguko wa dakika 40 alichoma kalori 690. Tatua mfumo\(\left\{\begin{array}{l}{15 e+30 c=435} \\ {30 e+40 c=690}\end{array}\right.\) kwa e, idadi ya kalori anayowaka kwa kila dakika kwenye mkufunzi wa elliptical, na cc, idadi ya kalori anayowaka kwa kila dakika ya mafunzo ya mzunguko.
Stephanie aliondoka Riverside, California, akiendesha gari lake kaskazini kwenye Interstate 15 kuelekea Salt Lake City kwa kasi ya maili 56 kwa saa. Nusu saa moja baadaye, Tina aliondoka Riverside katika gari lake kwenye njia sawa na Stephanie, akiendesha gari maili 70 kwa saa. Tatua mfumo\(\left\{\begin{array}{l}{56 s=70 t} \\ {s=t+\frac{1}{2}}\end{array}\right.\)
- kwa t kujua muda gani itachukua Tina kupata hadi Stephanie.
- thamani ya ss ni nini, idadi ya masaa Stephanie itakuwa inaendeshwa kabla Tina upatikanaji wa samaki hadi yake?
- Jibu
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- \(t=2\)masaa
- \(s=2 \frac{1}{2}\)masaa
Mazoezi ya kuandika
Tatua mfumo wa equations
\(\left\{\begin{array}{l}{x+y=10} \\ {x-y=6}\end{array}\right.\)
- kwa kuchora picha.
- kwa ubadilishaji.
- Ni njia ipi unayopendelea? Kwa nini?
Tatua mfumo wa equations
\(\left\{\begin{array}{l}{3 x+y=12} \\ {x=y-8}\end{array}\right.\) kwa kubadilisha na kuelezea hatua zako zote kwa maneno.
- Jibu
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Majibu yatatofautiana.
Self Check
Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.
b Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?