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Math Help - integer solutions of equation

  1. #1
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    integer solutions of equation

    "Express all integer solutions in terms of n to the equation 840x+354y=6n, where n is natural." please
    First I used the highest common factor method to find solutions for 840x+354y=6
    solutions are
    x=354m-8
    y=19-840m
    not sure what to do about 6n.

    I really need an answer for this one please, anything you have that might help would be greatly appreciated.
    Last edited by Rubberduckzilla; May 28th 2009 at 04:12 AM. Reason: slow response
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  2. #2
    Newbie jaco's Avatar
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    gcd(840,354)=6
    thus 6=a(840)+b(354) for some a,b both integers
    this solves to a=-8 and b=19
    therefore if you have 6n=840x+354y then i suppose x=-8n and y=19n
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  3. #3
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    Quote Originally Posted by jaco View Post
    if you have 6n=840x+354y then i suppose x=-8n and y=19n
    That gives you one solution for each value of n. If you want all the solutions then you need to use the fact that the least common multiple of 354 and 840 is 140\times354 = 59\times840\ (=49560). The general solution is then x = 59k-8n and y = 19n-140k, for any integer k.
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