Question 334129
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Rearrange your first equation so that it, like the other one, becomes *[tex \Large y] expressed as a function of *[tex \Large x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ (y\ -\ 6)\ =\ 36]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 6\ =\ x^2\ -\ 36]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x^2\ -\ 42]


Now set the two things that are equal to *[tex \Large y] equal to each other.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 42\ =\ -x^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ =\ 42]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \pm\sqrt{21}]


Then by substitution into the second equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -21]


Hence, the solution set is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \{(\sqrt{21},-21),\,(-\sqrt{21},-21)\}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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