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Math Help - Need help with solving algebraically

  1. #1
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    Post Need help with solving algebraically

    Solve algebraically

    2x -7y = 25

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  2. #2
    Moo
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    Hello,

    I suppose you have to solve it in \mathbb{Z} ...

    Well, Bézout's identity let you write :

    \exists x',y' \in \mathbb{Z} such as 2x'-7y'=1 as 2 and 7 are relatively prime numbers.

    So find a particular solution :

    2*4-7*1=1

    ->2*100-7*25=25

    x=100 and y=25 are particular solutions.

    Then, write 2x-7y=2*100-7*25 (=25)

    -> 2(x-100)=7(y-25)

    As 2 and 7 are relatively prime numbers, 2 divides (y-25) and 7 divides (x-100)

    We can say that y-25=2k --> 2(x-100)=14k --> x-100=7k

    S=\{\underbrace{100+7k}_{x} \ ; \ \underbrace{25+2k}_{y} \} \ , \ k \in \mathbb{Z}
    Last edited by Moo; September 1st 2008 at 08:08 AM.
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