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how would i solve ax + by = c

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I am assuming that a,b, and c are constants and you are attempting to solve for either the variable x or y.  in that case we can look at solving for each.
 
Y: to isolate (y), we must first move the (x) term to the right side of the equal by subtracting (ax) from both sides giving us [by = c - ax]. Then, we can divide both sides by (b) to isolate (y) on its own giving us the result of [y=(c - ax)/b)].
 
In order to solve for (x) you would follow the same process but isolate x instead which would render [x=(c-by)/a].