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I'm currently doing a project and for part of it I've been looking at rational solutions to linear eqautions in two vaiables, i.e. $ax+by=c$. I'd like to add a bit about what we can use these types of equations and their solutions for but can't find anything on the internet. Surely there's more to them than just finding $x$ and $y$. Are there any interesting uses for these types of equations?

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    If $b=0$, $y$ can be anything and $x=\frac{c}{a} \quad (a \ne 0)$. If $a$ and $b$ are $0$, so $x$ and $y$ can be anything.2011-11-11

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