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28 June, 03:29

Solve the following system of equations?

x + 3y - z = 2

x - 2y + 3z = 7

x + 2y - 5z = - 21

a) (2, 3, 5)

b) (-2, 3, 5)

c) (2, - 3, 5)

d) (2, - 3, 5)

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Answers (1)
  1. 28 June, 05:44
    0
    1x + 3y - 1z = 2 ⇒ 1x + 3y - 1z = 2

    1x - 2y + 3z = 7 ⇒ 1x - 2y + 3z = 7

    1x + 2y - 5z = - 21 5y - 4z = - 5

    5y - 4z = - 5 ⇒ - 20y + 16z = 20

    1x + 3y - 1z = 2 - 4y + 8z = - 28 ⇒ - 20y - 40z = - 140 1x - 2y + 3z = 7 ⇒ 1x - 2y + 3z = 7 - 24z = - 120

    1x + 2y - 5z = - 21 ⇒ 1x + 2y - 5z = - 21 - 24 - 24

    -4y + 8z = - 28 z = 5

    5y - 4 (5) = - 5

    5y - 20 = - 5

    +20 + 20

    5y = 15

    5 5

    y = 3

    x + 3 (3) - 5 = 2

    x + 9 - 5 = 2

    x + 4 = 2

    -4 - 4

    x = - 2

    (x, y, z) = (-2, 3, 5)

    The solution to the answer is B. (-2, 3, 5).
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