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23 June, 15:41

X+y+z=2

x+2y-z=5

2x+y-z=5

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Answers (1)
  1. 23 June, 17:47
    0
    Answer: [3] x = 2y - 3z - 6

    / / Plug this in for variable x in equation [1]

    [1] (2y-3z-6) + y + z = 2

    [1] 3y - 2z = 8

    / / Plug this in for variable x in equation [2]

    [2] 2• (2y-3z-6) + y - z = 5

    [2] 5y - 7z = 17

    / / Solve equation [2] for the variable y

    [2] 5y = 7z + 17

    [2] y = 7z/5 + 17/5

    / / Plug this in for variable y in equation [1]

    [1] 3• (7z/5+17/5) - 2z = 8

    [1] 11z/5 = - 11/5

    [1] 11z = - 11

    / / Solve equation [1] for the variable z

    [1] 11z = - 11

    [1] z = - 1

    / / By now we know this much:

    x = 2y-3z-6

    y = 7z/5+17/5

    z = - 1

    / / Use the z value to solve for y

    y = (7/5) (-1) + 17/5 = 2

    / / Use the y and z values to solve for x

    x = 2 (2) - 3 (-1) - 6 = 1

    Solution:

    {x, y, z} = {1,2,-1}
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