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Math Help - System of equations in 3 variables.

  1. #1
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    System of equations in 3 variables.

    1.) 2x + 10y + 6z = 8
    x + 5y + 3z = -2
    x + y + z = -4


    Help! Thanks.
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  2. #2
    Super Member Bacterius's Avatar
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    First equation :

    2x + 10y + 6z = 8

    Can be written : 10y + 6z = 8 - 2x

    And may also be written : 5y + 3z = 4 - x

    Substitute the left-hand-side into the second equation :

    x + 5y + 3z = -2

    Becomes :

    x + (4 - x) = -2

    Which simplifies to 4 = -2

    There is something terribly wrong with your system, you are sure you didn't make an error while copying them on the forum ?

    EDIT : ahah good working mathceleb, didn't think about the discriminant. By the way, is it correct to say that since his equation simplifies to -4 = 2, there cannot exist any solutions ? Or is it better to use the discriminant ?
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  3. #3
    Senior Member
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    Quote Originally Posted by kelsikels View Post
    1.) 2x + 10y + 6z = 8
    x + 5y + 3z = -2
    x + y + z = -4


    Help! Thanks.
    No solution exists to your system, because your discriminant = 0.


    See here for the math behind my answer using Cramer's Rule:

    3 unknown Cramer's Rule
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