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Math Help - Solving for variables

  1. #1
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    Post Solving for variables

    Given the system of equations, solve for x,y,z.

    2x + y + z = 6
    x + 2y + z = 12
    x + y + 2z = 24

    Thanks!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Subract the first two equations from one another

    2x+y+z=16
    -(x+2y+z)=-12
    =x-y=4

    solve for x in the equation

    x=y+4

    go back and substitute for x and reapeat the process until you have completely solve the system.

    Does that help?
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  3. #3
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    Post

    ok...I plugged in x to find that y = -12 + z.
    Is this correct?
    Then, would z = y + 12? How will I find the numerical values of x,y, and z?
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  4. #4
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    Make your life easier and simplify where you can.

    (x + y + 2z) - (x + 2y + z) = 12

    z - y = 12

    (x + 2y + z) - (2x + y + z) = 6

    y - x = 6

    (x + y + 2z) - (2x + y + z) = 18

    z - x = 18

    Now just keep substituting.

    x + y + 2z = 24

    (z - 18) + (z - 12) + 2z = 24

    4z - 30 = 24

    z = \frac{27}2
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