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-   -   Systems of equations with 3 variables (https://www.askmehelpdesk.com/showthread.php?t=277552)

  • Nov 5, 2008, 05:44 PM
    Flute09
    Systems of equations with 3 variables
    How do you solve systems of equations with 3 variables? And what if one of the equations only has 2 of the variables?
    Example:
    1) 2x+3y-4z=20
    2) 3x-2y+z=12
    3) 5x-2z=4

    Don't try to solve this one, I just made it up to give you an example.
  • Nov 5, 2008, 05:53 PM
    Credendovidis
    1) 2x+3y-4z=20
    2) 3x-2y+z=12
    3) 5x-2z=4

    To solve x , y, and z : to solve this you have to reduce this to 2 variables (x and y).

    As (3) 5x-2z=4 --> -2z=4-5x --> 2z=5x-4 --> z=2,5x-2
    So z=2,5x-2 and therefore 4z=10x-8

    Now use these solutions for z in (1) and (2) and solve x and y

    1) 2x+3y-4z=20 --> 2x+3y-(10x-8)=20
    2) 3x-2y+z=12 ----> 3x-2y+(2,5x-2)=12

    Succes !

    :)

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