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5.3E: Mazoezi

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    177360
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    Mazoezi hufanya kamili

    Tatua Mfumo wa Equations kwa Kuondoa

    Katika mazoezi yafuatayo, tatua mifumo ya equations kwa kuondoa.

    Zoezi\(\PageIndex{1}\)

    \(\left\{\begin{array}{l}{5 x+2 y=2} \\ {-3 x-y=0}\end{array}\right.\)

    Zoezi\(\PageIndex{2}\)

    \(\left\{\begin{array}{l}{-3 x+y=-9} \\ {x-2 y=-12}\end{array}\right.\)

    Jibu

    \((6,9)\)

    Zoezi\(\PageIndex{3}\)

    \(\left\{\begin{array}{l}{6 x-5 y=-1} \\ {2 x+y=13}\end{array}\right.\)

    Zoezi\(\PageIndex{4}\)

    \(\left\{\begin{array}{l}{3 x-y=-7} \\ {4 x+2 y=-6}\end{array}\right.\)

    Jibu

    \((-2,1)\)

    Zoezi\(\PageIndex{5}\)

    \(\left\{\begin{array}{l}{x+y=-1} \\ {x-y=-5}\end{array}\right.\)

    Zoezi\(\PageIndex{6}\)

    \(\left\{\begin{array}{l}{x+y=-8} \\ {x-y=-6}\end{array}\right.\)

    Jibu

    \((-7,-1)\)

    Zoezi\(\PageIndex{7}\)

    \(\left\{\begin{array}{l}{3 x-2 y=1} \\ {-x+2 y=9}\end{array}\right.\)

    Zoezi\(\PageIndex{8}\)

    \(\left\{\begin{array}{l}{-7 x+6 y=-10} \\ {x-6 y=22}\end{array}\right.\)

    Jibu

    \((-2,-4)\)

    Zoezi\(\PageIndex{9}\)

    \(\left\{\begin{array}{l}{3 x+2 y=-3} \\ {-x-2 y=-19}\end{array}\right.\)

    Zoezi\(\PageIndex{10}\)

    \(\left\{\begin{array}{l}{5 x+2 y=1} \\ {-5 x-4 y=-7}\end{array}\right.\)

    Jibu

    \((-1,3)\)

    Zoezi\(\PageIndex{11}\)

    \(\left\{\begin{array}{l}{6 x+4 y=-4} \\ {-6 x-5 y=8}\end{array}\right.\)

    Zoezi\(\PageIndex{12}\)

    \(\left\{\begin{array}{l}{3 x-4 y=-11} \\ {x-2 y=-5}\end{array}\right.\)

    Jibu

    \((-1,2)\)

    Zoezi\(\PageIndex{13}\)

    \(\left\{\begin{array}{l}{5 x-7 y=29} \\ {x+3 y=-3}\end{array}\right.\)

    Zoezi\(\PageIndex{14}\)

    \(\left\{\begin{array}{l}{6 x-5 y=-75} \\ {-x-2 y=-13}\end{array}\right.\)

    Jibu

    \((-5,9)\)

    Zoezi\(\PageIndex{15}\)

    \(\left\{\begin{array}{l}{-x+4 y=8} \\ {3 x+5 y=10}\end{array}\right.\)

    Zoezi\(\PageIndex{16}\)

    \(\left\{\begin{array}{l}{2 x-5 y=7} \\ {3 x-y=17}\end{array}\right.\)

    Jibu

    \((6,1)\)

    Zoezi\(\PageIndex{17}\)

    \(\left\{\begin{array}{l}{5 x-3 y=-1} \\ {2 x-y=2}\end{array}\right.\)

    Zoezi\(\PageIndex{18}\)

    \(\left\{\begin{array}{l}{7 x+y=-4} \\ {13 x+3 y=4}\end{array}\right.\)

    Jibu

    \((-2,10)\)

    Zoezi\(\PageIndex{19}\)

    \(\left\{\begin{array}{l}{-3 x+5 y=-13} \\ {2 x+y=-26}\end{array}\right.\)

    Zoezi\(\PageIndex{20}\)

    \(\left\{\begin{array}{l}{3 x-5 y=-9} \\ {5 x+2 y=16}\end{array}\right.\)

    Jibu

    \((2,3)\)

    Zoezi\(\PageIndex{21}\)

    \(\left\{\begin{array}{l}{4 x-3 y=3} \\ {2 x+5 y=-31}\end{array}\right.\)

    Zoezi\(\PageIndex{22}\)

    \(\left\{\begin{array}{l}{4 x+7 y=14} \\ {-2 x+3 y=32}\end{array}\right.\)

    Jibu

    \((-7,6)\)

    Zoezi\(\PageIndex{23}\)

    \(\left\{\begin{array}{l}{5 x+2 y=21} \\ {7 x-4 y=9}\end{array}\right.\)

    Zoezi\(\PageIndex{24}\)

    \(\left\{\begin{array}{l}{3 x+8 y=-3} \\ {2 x+5 y=-3}\end{array}\right.\)

    Jibu

    \((-9,3)\)

    Zoezi\(\PageIndex{25}\)

    \(\left\{\begin{array}{l}{11 x+9 y=-5} \\ {7 x+5 y=-1}\end{array}\right.\)

    Zoezi\(\PageIndex{26}\)

    \(\left\{\begin{array}{l}{3 x+8 y=67} \\ {5 x+3 y=60}\end{array}\right.\)

    Jibu

    \((9,5)\)

    Zoezi\(\PageIndex{27}\)

    \(\left\{\begin{array}{l}{2 x+9 y=-4} \\ {3 x+13 y=-7}\end{array}\right.\)

    Zoezi\(\PageIndex{28}\)

    \(\left\{\begin{array}{l}{\frac{1}{3} x-y=-3} \\ {x+\frac{5}{2} y=2}\end{array}\right.\)

    Jibu

    \((-3,2)\)

    Zoezi\(\PageIndex{29}\)

    \(\left\{\begin{array}{l}{x+\frac{1}{2} y=\frac{3}{2}} \\ {\frac{1}{5} x-\frac{1}{5} y=3}\end{array}\right.\)

    Zoezi\(\PageIndex{30}\)

    \(\left\{\begin{array}{l}{x+\frac{1}{3} y=-1} \\ {\frac{1}{2} x-\frac{1}{3} y=-2}\end{array}\right.\)

    Jibu

    \((-2,3)\)

    Zoezi\(\PageIndex{31}\)

    \(\left\{\begin{array}{l}{\frac{1}{3} x-y=-3} \\ {\frac{2}{3} x+\frac{5}{2} y=3}\end{array}\right.\)

    Zoezi\(\PageIndex{32}\)

    \(\left\{\begin{array}{l}{2 x+y=3} \\ {6 x+3 y=9}\end{array}\right.\)

    Jibu

    ufumbuzi mkubwa sana

    Zoezi\(\PageIndex{33}\)

    \(\left\{\begin{array}{l}{x-4 y=-1} \\ {-3 x+12 y=3}\end{array}\right.\)

    Zoezi\(\PageIndex{34}\)

    \(\left\{\begin{array}{l}{-3 x-y=8} \\ {6 x+2 y=-16}\end{array}\right.\)

    Jibu

    ufumbuzi mkubwa sana

    Zoezi\(\PageIndex{35}\)

    \(\left\{\begin{array}{l}{4 x+3 y=2} \\ {20 x+15 y=10}\end{array}\right.\)

    Zoezi\(\PageIndex{36}\)

    \(\left\{\begin{array}{l}{3 x+2 y=6} \\ {-6 x-4 y=-12}\end{array}\right.\)

    Jibu

    ufumbuzi mkubwa sana

    Zoezi\(\PageIndex{37}\)

    \(\left\{\begin{array}{l}{5 x-8 y=12} \\ {10 x-16 y=20}\end{array}\right.\)

    Zoezi\(\PageIndex{38}\)

    \(\left\{\begin{array}{l}{-11 x+12 y=60} \\ {-22 x+24 y=90}\end{array}\right.\)

    Jibu

    haiendani, hakuna ufumbuzi

    Zoezi\(\PageIndex{39}\)

    \(\left\{\begin{array}{l}{7 x-9 y=16} \\ {-21 x+27 y=-24}\end{array}\right.\)

    Zoezi\(\PageIndex{40}\)

    \(\left\{\begin{array}{l}{5 x-3 y=15} \\ {y=\frac{5}{3} x-2}\end{array}\right.\)

    Jibu

    haiendani, hakuna ufumbuzi

    Zoezi\(\PageIndex{41}\)

    \(\left\{\begin{array}{l}{2 x+4 y=7} \\ {y=-\frac{1}{2} x-4}\end{array}\right.\)

    Kutatua Matumizi ya Mifumo ya Equations na Kuondoa

    Katika mazoezi yafuatayo, tafsiri kwa mfumo wa equations na kutatua.

    Zoezi\(\PageIndex{42}\)

    Jumla ya namba mbili ni 65. Tofauti yao ni 25. Kupata idadi.

    Jibu

    Idadi ni 20 na 45.

    Zoezi\(\PageIndex{43}\)

    Jumla ya namba mbili ni 37. Tofauti yao ni 9. Kupata idadi.

    Zoezi\(\PageIndex{44}\)

    Jumla ya namba mbili ni -27. Tofauti yao ni -59. Kupata idadi.

    Jibu

    Namba ni 16 na -43.

    Zoezi\(\PageIndex{45}\)

    Jumla ya namba mbili ni -45. Tofauti yao ni -89. Kupata idadi.

    Zoezi\(\PageIndex{46}\)

    Andrea ni kununua baadhi ya mashati mpya na sweta. Anaweza kununua mashati 3 na jasho 2 kwa $114 au anaweza kununua mashati 2 na jasho 4 kwa $164. Je! Shati ina gharama gani? Je! Sweta ina gharama gani?

    Jibu

    Shati inachukua $16 na jasho lina gharama $33.

    Zoezi\(\PageIndex{47}\)

    Peter ni kununua vifaa vya ofisi. Anaweza kununua paket 3 za karatasi na staplers 4 kwa $40 au anaweza kununua paket 5 za karatasi na staplers 6 kwa $62. Je! Mfuko wa karatasi una gharama gani? Kiasi gani cha gharama cha gharama?

    Zoezi\(\PageIndex{48}\)

    Jumla ya sodiamu katika mbwa 2 za moto na vikombe 3 vya jibini la Cottage ni 4720 mg. Jumla ya sodiamu katika mbwa 5 za moto na vikombe 2 vya jibini la Cottage ni 6300 mg. Ni kiasi gani cha sodiamu katika mbwa wa moto? Ni kiasi gani cha sodiamu katika kikombe cha jibini la Cottage?

    Jibu

    Kuna 860 mg katika mbwa wa moto. Kuna 1,000 mg katika kikombe cha jibini la Cottage.

    Zoezi\(\PageIndex{49}\)

    Idadi ya kalori katika mbwa 2 za moto na vikombe 3 vya jibini la Cottage ni kalori 960. Idadi ya kalori katika mbwa 5 za moto na vikombe 2 vya jibini la Cottage ni kalori 1190. Ni kalori ngapi katika mbwa wa moto? Ni kalori ngapi katika kikombe cha jibini la Cottage?

    Chagua Njia rahisi zaidi ya Kutatua Mfumo wa Ulinganisho wa Mstari

    Katika mazoezi yafuatayo, chagua kama itakuwa rahisi zaidi kutatua mfumo wa equations kwa kubadilisha au kuondoa.

    Zoezi\(\PageIndex{50}\)
    1. \( \left\{\begin{array}{l}{8 x-15 y=-32} \\ {6 x+3 y=-5}\end{array}\right.\)
    2. \(\left\{\begin{array}{l}{x=4 y-3} \\ {4 x-2 y=-6}\end{array}\right.\)
    Jibu
    1. kuondoa
    2. badala
    Zoezi\(\PageIndex{51}\)
    1. \(\left\{\begin{array}{l}{y=7 x-5} \\ {3 x-2 y=16}\end{array}\right.\)
    2. \(\left\{\begin{array}{l}{12 x-5 y=-42} \\ {3 x+7 y=-15}\end{array}\right.\)
    Zoezi\(\PageIndex{52}\)
    1. \(\left\{\begin{array}{l}{y=4 x+9} \\ {5 x-2 y=-21}\end{array}\right.\)
    2. \(\left\{\begin{array}{l}{9 x-4 y=24} \\ {3 x+5 y=-14}\end{array}\right.\)
    Jibu
    1. badala
    2. kuondoa
    Zoezi\(\PageIndex{53}\)
    1. \(\left\{\begin{array}{l}{14 x-15 y=-30} \\ {7 x+2 y=10}\end{array}\right.\)
    2. \(\left\{\begin{array}{l}{x=9 y-11} \\ {2 x-7 y=-27}\end{array}\right.\)

    kila siku Math

    Zoezi\(\PageIndex{54}\)

    Katika saa moja Norris unaweza mstari 3 maili mkondo dhidi ya sasa. Katika kiasi kama hicho cha muda anaweza mstari 5 maili chini ya mto, na sasa. Tatua mfumo. \(\left\{\begin{array}{l}{r-c=3} \\ {r+c=5}\end{array}\right.\)

    1. kwa r, kasi yake makasia katika maji bado.
    2. Kisha kutatua kwa c, kasi ya mto wa sasa.
    Jibu
    1. r=4
    2. c=1
    Zoezi\(\PageIndex{55}\)

    Josie anataka kufanya 10 paundi ya uchaguzi mchanganyiko kwa kutumia karanga na zabibu, na yeye anataka gharama ya jumla ya uchaguzi mchanganyiko kuwa $54. Nuts gharama $6 kwa pauni na zabibu gharama $3 kwa pauni. Tatua mfumo wa\(\left\{\begin{array}{l}{n+r=10} \\ {6 n+3 r=54}\end{array}\right.\) kupata n, idadi ya paundi ya karanga, na rr, idadi ya paundi ya zabibu anapaswa kutumia.

    Mazoezi ya kuandika

    Zoezi\(\PageIndex{56}\)

    Tatua mfumo
    \(\left\{\begin{array}{l}{x+y=10} \\ {5 x+8 y=56}\end{array}\right.\)

    1. kwa ubadilishaji
    2. kwa kuchora picha
    3. Ni njia gani unayopendelea? Kwa nini?
    Jibu
    1. (8, 2)

    Picha hii ni grafu inayoonyesha ufumbuzi wa mfumo “x plus y sawa na 10" na 5x plus 8y sawa 56. Suluhisho ni kwenye ndege ya kuratibu x, y. Mishale miwili inakabiliana kwenye pointi 8 na 2.

    3. Majibu yatatofautiana.

    Zoezi\(\PageIndex{57}\)

    Tatua mfumo\(\left\{\begin{array}{l}{x+y=-12} \\ {y=4-\frac{1}{2} x}\end{array}\right.\)

    1. kwa ubadilishaji
    2. kwa kuchora picha
    3. Ni njia ipi unayopendelea? Kwa nini?

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Takwimu hii inaonyesha meza yenye safu nne na nguzo nne. Nguzo zimeandikwa, “Ninaweza...,” “Kwa ujasiri.” “Kwa msaada fulani.” na “Hapana - siipati.” Safu pekee iliyojaa seli chini yake imeandikwa “Naweza...” Inasoma, “tatua mfumo wa equations kwa kuondoa.” “Tatua matumizi ya mifumo ya equations kwa kuondoa.” na “chagua njia rahisi zaidi ya kutatua mfumo wa equations linear.”

    b Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?