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.