Can someone "give me a feel" for how extraneous solutions arise in curve intersection problems. E.g. why doesn't setting the z's equal to each other always work? The impetus behind this question is PS4-2a. I will post the question and their solution.

Question

anonymous · Answer

Here is the problem and their solution. Thanks in advance.

deltanu · Answer

This is a property of solving equations in general. Just read this wiki page and it's got a very clear explanation: https://en.wikipedia.org/wiki/Extraneous_and_missing_solutions