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

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To solve the equation 8ab + 7b + 3a = c for either a or b, it's important to recognize that there are infinitely many solutions, necessitating a free variable. By designating a as the free variable, b can be expressed in terms of a. Since a and b are integers and there is a unique solution for the equation to equal c, additional equations may be required to pinpoint specific values. The discussion also mentions the potential use of matrices or differential equations, although their direct applicability is questioned. Ultimately, finding another equation equal to c could be essential for determining specific integer values 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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