Question

x + y + 2z = 4
2x - 3y + z = 0
5x - y - z = 3

Answer 1

Explicação passo a passo:

X + y + 2z = 4>>>>>>>>>>>>1

2x - 3y + z = 0>>>>>>>>>>>>2

5x - y - z = 3>>>>>>>>>>>>3

calculando >>>>>>>>>>1 e >>>>>>>>2

X + y + 2z = 4>>>>>>>>>>>>1 ( vezes - 2)

2x - 3y + z = 0>>>>>>>>>>>>2

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- 2x - 2y - 4z = - 8

2x - 3y + 1z = 0

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// - 5y - 3z = -8 ( - 1)

5y + 3z = 8 >>>>>>>>>>>>>>>>4

calculando >>>>>>2 e >>>>>>>3

2x - 3y + z = 0>>>>>>>>>>>>2 ( vezes -5)

5x - y - z = 3>>>>>>>>>>>>3 ( vezes 2 )

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- 10x + 15y - 5z = 0

10x - 2y - 2z = 6

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// 13y - 7z = 6>>>>>>>>>>>>5

calculando >>>>>>>>>>4 e >>>>>>>>>>.5

5y + 3z = 8>>>>>>>>>>>>4( vezes - 13 )

13y - 7z = 6>>>>>>>>>>>>5 (vezes 5 )

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- 65 y - 39z = -104

+ 65y -35z = 30

=======================

// - 74z = - 74

74z = 74

z = 74/74 =1 :>>>>>>>>>>resposta z

substitui em >>>>>>>>>>4 o valor de z por 1 >>>>

5y + 3z = 8 >>>>>>>>>>>>>>>>4

5y + 3 ( 1 ) = 8

5y + 3 = 8

5y = 8-3

5y = 5

y = 5/5 = 1 >>>>>resposta

em >>>>>>1 acima substitui y = 1 e z =1

x + y + 2z =4

x + 1 +2 ( 1) = 4

x + 1 + 2 = 4

x + 3 = 4

x = 4 - 3

x = 1 >>>>>resposta

Answer 2

Vamos lá.

5x - y - z = 3   (I)

x + y + 2z = 4 (II)

2x - 3y + z = 0 (III)

de (I)

z = 5x - y - 3

de (II) vem

x + y + 10x - 2y - 6 = 4

11x - y = 10 (IV)

de (III) vem

2x - 3y + 5x - y - 3 = 0

7x - 4y = 3 (V)

11x - y = 10 (IV)

44x - 4y = 40

37x = 37

x = 1

7 - 4y = 3

4y = 4

y = 1

z = 5x - y - 3 = 5 - 1 - 3 = 1

S = (1, 1, 1)