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[Community Question] Algebra-Precalculus: How to find the integer solution for $6x + 25 = 7y$?

One of our user asked:

When I type this equation ($6x + 25 = 7y$) into WolframAlpha, it is able to tell me that the integer solution for this equation is:

$x = 7n + 4$, $y = 6n + 7$, where n in the set of all integers

How can I arrive at this solution on my own?


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