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