I'll add two more cents here. I've had very good luck using ImplicitEquation to allow me to write problems that would otherwise not have worked, with the caveats that Paul indicates. In practice it's easy to construct a problem that is mathematically sufficiently intractible that either the correct or student answers don't quite work as they should. But I think that's more a commentary on the need to be careful using ImplicitEquation rather than a statement that it shouldn't be used. And where the ImplicitPlane module will work instead it's far more robust. There's something about linearity that makes life much easier...
Cheers,
Gavin