There can be more than one solution of the equations are degenerate. e.g., if you actually have less equations than variables. In this case those all the equations are independent.
By using conductances it is a simple linear equation Ax = b which has a solution, if it exists, as x = A^(-1)*b. You can use the generalized inverse to get a least squares approximation(Ax ~= b) if the solution does not exist.
It's possible someone got a sign backwards if they gave the same magnitude.