Solving Implicit Equations for y in Terms of x

[Fuz]

How do you go about solving implicit equations for y in terms of x that look like these?

y² + yx = 1

and

y³ + yx = 1

or even more complicated implicit equations.

I'm taking AP Calculus AB this year and am just curious how this is done.

Here are the solutions from Wolframalpha:
http://www.wolframalpha.com/input/?i=y^2+%2B+yx+%3D+1
http://www.wolframalpha.com/input/?i=y^3+%2B+xy+%3D+1

 

[Number Nine]

You just need to play with the function until you find an answer. Use the usual rules of arithmetic. You aren't going to encounter any situations in AP Calculus where you would need to solve a hugely complex implicit function for y.

 

[Fuz]

Can you show me the steps for one of them? I've already tried solving them myself, but got nowhere.

 

[Mentallic]

Can you show me the steps for one of them? I've already tried solving them myself, but got nowhere.

By solve I assume you mean to express the implicit function in the form y=f(x). Well, for the first you can use the quadratic formula or complete the square (it's basically equivalent) and for the second you'll need to use the cubic formula.