Question 1079453
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ y^2\ =\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x^2\ -\ 9]


Solve the second equation for *[tex \Large x^2] and then substitute into the first equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (y\ +\ 9)^2\ +\ y^2\ =\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y^2\ +\ 18y\ +\ 81\ +\ y^2\ =\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2y^2\ +\ 18y\ +\ 80\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y^2\ +\ 9y\ +\ 40\ =\ 0]


But *[tex \Large 9^2\ -\ 4(1)(40)\ <\ 0]


Hence, no real solutions.  The solution set of the system is *[tex \Large \emptyset]


*[illustration NonLinearSystem]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  


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