If 8ab+7b+3a=c, whats the best way to figure out either a or b

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The equation 8ab + 7b + 3a = c can be solved for either variable a or b, given that c is a known integer. The discussion highlights that since there are infinitely many solutions, one variable can be treated as a free variable, allowing for the other to be expressed in terms of it. Specifically, setting a as the free variable simplifies the process of solving for b. Additionally, the need for another equation equal to c is suggested to narrow down the solutions to a unique pair of integers for a and b.

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C is a known number, therefore I would only need to solve for a or b. Whats the best way to solve this, a few things come to mind, using a matrix or differential equations, but I'm not sure how they are applicable to this situation.
 
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There are infinitely many solutions. So you're going to have a free variable. So let a be the free variable, then you can easily solve for b.
 
I should have mentioned, a and b are integers, and there is only one solution for a and b to get c. I may be able to find another equation that is equal to c. Would I need this in order to solve the equation?
 

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