Solving a nonlinear system with parameters

[KevinL]

I'm doing my economics thesis on game theory, and need to solve a system of nonlinear equations (these will be the reaction functions). Unfortunately, I have no idea how to solve it explicitly--indeed, I am a bit worried its impossible with the parameters. It is rather symmetric though.

The system is as such:

a₀x² + a₁xy + a₂x + a₃y + a₄ = 0

b₀y² + b₁xy + b₂x + b₃y + b₄ = 0

Any help pointing me in the right direction is much appreciated!

 

[gsal]

If all 'a' and 'b' constants are known, you can isolate, say, y from the first equation and insert the resulting into the second equation...a few line of expanding everything and multiplying, etc., you will end up with a forth degree polynomial for x