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Solutions of a System of Nonlinear Equations

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Give an example of a nonlinear system of two equations in two unknowns having:

(a) exactly 6 solutions Verify your work and give points of intersection.

(b) exactly 7 solutions Verify your work and give points of intersection.

Based on your work, how would you devise a method for finding such a system having exactly n solutions?

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Solution Preview

(a) The following system has exactly 6 solutions:

y = (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)
y = 0

The solutions are ...

Solution Summary

We show how to devise a system of two nonlinear equations in two variables with six, seven, or an arbitrary number of solutions.

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