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Diketahui system persamaan linear 3 variabel berikut: x 2 ​ − y 3 ​ + z 1 ​ = 2 x 1 ​ + y 5 ​ − z 1 ​ = − 5 x 4 ​ + y 1 ​ − z 3 ​ = − 4 Nilai dari y x ⋅ z ​ = ...

Diketahui system persamaan linear 3 variabel berikut:

Nilai dari

  1. 18,10

  2. 18,15

  3. 18,20

  4. 18,25

  5. 18,75

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Misalkan : Maka, 2p – 3q + r = 2….(i) p + 5q -4r =-5…(ii) 4p + q -3r =-4…(iii) Eliminasi p dari (i) dan (ii) Eliminasi p dari (ii) dan (iii) lalu,

Misalkan : 1 over straight x equals straight p comma space 1 over straight y equals straight q comma space 1 over straight z equals straight r

Maka, 2p – 3q + r = 2….(i)
p + 5q -4r =-5…(ii)
4p + q -3r =-4…(iii)
Eliminasi p dari (i) dan (ii)

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 straight p space – space 3 straight q space plus space straight r space equals space 2 straight p space plus space 5 straight q space minus 4 straight r space equals negative 5 space rightwards arrow cross times 2 rightwards arrow bottom enclose 2 straight p space plus space 10 straight q space minus 8 straight r space equals negative 10 end enclose minus space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 13 straight q space plus space 9 straight r space equals 12 horizontal ellipsis......... left parenthesis iv right parenthesis

Eliminasi p dari (ii) dan (iii)

straight p plus 5 straight q minus 4 straight r equals negative 5 space rightwards arrow cross times 4 rightwards arrow 4 straight p plus space 20 straight q minus 16 straight r equals negative 20 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bottom enclose 4 straight p plus space straight q minus 3 straight r equals negative 4 space space minus end enclose space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 16 straight q space minus 13 straight r space equals negative 16 space horizontal ellipsis... left parenthesis straight v right parenthesis

lalu, fraction numerator straight x times straight z over denominator straight y end fraction equals fraction numerator negative 25 times begin display style 25 over 16 end style over denominator fraction numerator negative 25 over denominator 12 end fraction end fraction equals fraction numerator 25 times 25 times 12 over denominator 16 times 25 end fraction equals 300 over 13 equals 18 comma 75

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