Question 529048
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Any 2X2 system of the form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha_1x\ +\ \beta_1y\ =\ \gamma_1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha_2x\ +\ \beta_2y\ =\ \gamma_2]


Where


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \exists\,k\,\in\,\mathbb{R}\,|\,\alpha_1\,=\,k\alpha_2\text{ and }\beta_1\,=\,k\beta_2\text{ but }\gamma_1\,\neq\,k\gamma_2]


Is an inconsistent system with a null set solution set that graphs to a pair of parallel lines.


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