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Find all integer solutions of the equations: \begin{cases} 6x+21y&=&33 \\ 14x-49y&=&13 \end{cases}

I'm not sure how to find all integer solutions for a, but I know there are no integer solutions for b, because $\mbox{gcd}(14,49)=7$ and $7$ does not divide $13$.

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    In a), first step is to divide through by 3.2012-09-18
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    I know that. Which gives 2x+7y=11. By looking at it I can tell one integer solution is x=2 and y=1, but I don't know how to find all integer solutions.2012-09-18
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    Good. Now, solve for $x$ and figure out what $y$ has to do to make $x$ an integer.2012-09-19

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