1. The problem statement, all variables and given/known data Solver for n and m in the following equations: 2n + 6m [itex]\equiv[/itex] 2 (mod 10) n + m [itex]\equiv[/itex] -2 (mod 10) 2. Relevant equations 3. The attempt at a solution I've worked through several of these problems prior, including ones in the book and most take the form: 2n + 3m = 3 (mod 10) n + 3m = -2 (mod 10) or something similar, where it is easy to subtract one equation from the other and solve for one variable, then plug back in and solve for the other. Or cases where it's easy to multiply and then subtract. In this case though, my textbook explicitly says you cannot multiply the equation by a number that's not relatively prime with the modulus, so I'm at a loss for how to cancel out a variable to solve these equations. This multiplying / subtracting or adding method is all we've been shown. I would greatly appreciate some advice on how to approach the problem!