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Math Help - solving for 3 unknowns

  1. #1
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    solving for 3 unknowns

    c + ba = 30
    a + bc = 18

    SOLVE FOR a, b, c
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  2. #2
    MHF Contributor red_dog's Avatar
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    a,b,c are integers?
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  3. #3
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    Quote Originally Posted by red_dog View Post
    a,b,c are integers?
    I guess so..
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  4. #4
    MHF Contributor red_dog's Avatar
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    Adding and substracting the two equations we have
    \displaystyle \left\{\begin{array}{ll}(a-c)(b-1)=12\\(a+c)(b+1)=48\end{array}\right.
    So, b-1 must divide 12 and b+1 must divide 48.
    For example:
    b-1=1\Rightarrow b=2\Rightarrow b+1=3|48.
    Replacing b=2 in system we have
    \displaystyle \left\{\begin{array}{ll}a-c=12\\a=c=16\end{array}\right.\Rightarrow a=14,c=2.
    And so on...
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