Question 531618
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Given the system:


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


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


If 


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


then the system is inconsistent.


If 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \exists\ k\ | \alpha_1\ =\ {k}\alpha_2\text{ and }\beta_1\ =\ {k}\beta_2\text{ and }\gamma_1\ =\ {k}\gamma_2]


then the system is consistent and dependent.


If


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \not\exists\ k\ | \alpha_1\ =\ {k}\alpha_2\text{ and }\beta_1\ =\ {k}\beta_2]


then the system is consistent and independent.



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