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Solving a nonlinear system with parameters

  1. Sep 7, 2011 #1
    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, im 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!
  2. jcsd
  3. Sep 7, 2011 #2
    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
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