Thread: Functional dependency between equations

To begin with, I have to apologize: I'm not a native English speaker, and I'm currently studying math in my native language, so I'm not certain I've got my terms right. The problem is, Google can't find any information on this subject in my native language.

To put it bluntly, I have no idea what this question (literally translated by me) is getting at:
"Is there a functional dependency between the following two equations:
y1 = [a polynomial function of variables x1 and x2]
y2 = [a polynomial function of variables x1 and x2]"

Can there be something called "functional dependency" (or similar) between equations? The only sort of dependency I've run into so far is linear dependency in matrices, but I've no idea how I'd go about checking that here. Any clues as to common methods of checking "functional dependency" (if that is the right term) between equations?

I'd be grateful for any help.

Originally Posted by GrimRedeemer

To begin with, I have to apologize: I'm not a native English speaker, and I'm currently studying math in my native language, so I'm not certain I've got my terms right. The problem is, Google can't find any information on this subject in my native language.

To put it bluntly, I have no idea what this question (literally translated by me) is getting at:
"Is there a functional dependency between the following two equations:
y1 = [a polynomial function of variables x1 and x2]
y2 = [a polynomial function of variables x1 and x2]"

Can there be something called "functional dependency" (or similar) between equations? The only sort of dependency I've run into so far is linear dependency in matrices, but I've no idea how I'd go about checking that here. Any clues as to common methods of checking "functional dependency" (if that is the right term) between equations?

I'd be grateful for any help.

maybe this can help

After looking at the usage of the term there, I figured it simply meant whether there was a function f(y1) = y2 for any (x1, x2) that is a bijection, and solved it like that.

I got the right answer (they had a relatively simple quadratic dependency, once you reduced, combined and mashed them up a bit), although the lecturer apparently meant for us to just check whether the functions' Jacobian was singular, which would mean there was some sort of linear dependency. Seems I wasn't the only one confused by the question, few had managed to get any results.

Thank you.