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To solve the simultaneous congruences $$2n + 6m\equiv 2 \pmod{10}$$ and $$n + m\equiv -2 \pmod{10}$$

I tried to add the two congruences together so I got: $$3n + 7m\equiv 0 \pmod{10}$$ But I am not sure if that's right and if it is, what to do next to calculate the two separate variables. If the question is like $n\equiv x \pmod y$ then it's simple enough to calculate

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    How do you normally solve a system of two equations in two variables? What you did is right, but not especially useful....2012-07-06
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    Do you just treat them like any other equation? if you do, I get m=3/2 and n=-7/2 but that doesn't seem right.2012-07-06
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    Welcome to the site, Jason. I took the liberty of editing your post---hope it's okay. If you're going to stick around (and we hope you do), it would be a good idea to learn some LaTeX typesetting conventions for mathematics. An easy way to do this is to find a post that has something like you want to say, clicking on "edit" below the post and then looking at the "source" document in edit mode. The window in which you post your question or answer has help options just above and to the right.2012-07-06

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