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29 December, 20:58

Solve the system using substitution.

3x + 4y - z = 8

x - 5y + 2z = 24

5x + y - 2z = 30

The solution to the system of three linear equations is the ordered triple (x, y, z).

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Answers (1)
  1. 29 December, 21:19
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    Answer: x = 7, y = - 3, z = 1

    Step-by-step explanation:

    EQ 1: 3x + 4y - z = 8 solve for z

    +z - 8 + z - 8

    3x + 4y - 8 = z

    EQ 3: 5x + y - 2z = 30 substitute 3x + 4y - 8 for z and solve for x

    5x + y - 2 (3x + 4y - 8) = 30

    5x + y - 6x - 8y + 16 = 30

    -x - 7y + 16 = 30

    -16 - 16

    -x - 7y = 14

    +7y + 7y

    -x = 7y + 14

    x = - 7y - 14

    EQ 2: x - 5y + 2z = 24 substitute 3x+4y - 8 for z and - 7y - 14 for x

    (-7y - 14) - 5y + 2 (3x + 4y - 8) = 24

    -7y - 14 - 5y + 6 (-7y - 14) + 8y - 16 = 24

    -7y - 14 - 5y - 42y - 84 + 8y - 16 = 24

    -46y - 114 = 24

    +114 + 114

    -46y = 138

    :-46 : -46

    y = - 3

    x = - 7y - 14

    = - 7 (-3) - 14

    = 21 - 14

    = 7

    z = 3x + 4y - 8

    = 3 (7) + 4 (-3) - 8

    = 21 - 12 - 8

    = 1
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