Nonlinear system, manually computing imaginary solutions

The answer is not as important as how you arrived there, wolfram alpha can compute these. I would like to know how to solve manually.

I keep getting the equation from substitution(solved for formula 1, subbed into 2),

elimination yields nothing because there are no real roots, the graph is a circle within an ellipse.

Using the quadratic formula with the above equation gives me much different answers than wolfram.

I get Which does not make much sense.

Re: Nonlinear system, manually computing imaginary solutions

Another system I cannot solve manually is:

Due to the same reasons, I think I am forcing myself into extraneous solutions somehow :S

Re: Nonlinear system, manually computing imaginary solutions

Hello, Greymalkin!

We have: .

Substitute into [1]: .

. . . . . . . . . . . . . . .

Re: Nonlinear system, manually computing imaginary solutions

Hello agaibn, Greymalkin!

From [2]: .

Substitute into [1]: .

. .

. .

If , [2] becomes: .

If , [2] becomes: .

We have four solutions: .

Re: Nonlinear system, manually computing imaginary solutions

2 Attachment(s)

Re: Nonlinear system, manually computing imaginary solutions

First system has a circle & ellipse that do not interset:

http://mathhelpforum.com/attachment....1&d=1346118831

Second system has two real and two complex roots:

http://mathhelpforum.com/attachment....1&d=1346118898