Question 634169
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Pick an integer in the range *[tex \LARGE -12\ <\ x\ <\ 12].  Set *[tex \LARGE x] equal to that integer.


Pick an integer in the range *[tex \LARGE -12\ <\ y\ <\ 12].  Set *[tex \LARGE y] equal to that integer.


Then pick four other numbers to use for coefficients, they should be 4 different numbers and you can make some of them positive and some negtive.  I think you should pick small integers, but avoid zero.  I'm going to call these four numbers *[tex \LARGE \alpha_1,\,\beta_1,\,\alpha_2,\,and\ \beta_2] for purposes of discussion.


Take the first of the coefficients (*[tex \LARGE \alpha_1]) and multiply it by the value you chose for *[tex \LARGE x].  Take *[tex \LARGE \beta_1] and multiply it by the value you chose for *[tex \LARGE y].  Add the two products and we'll call the sum *[tex \LARGE \gamma_1].


Then write your first equation:


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


inserting the values for *[tex \LARGE \alpha_1,\,\beta_1\,and\,\gamma_1] but leaving the variables *[tex \LARGE x] and *[tex \LARGE y] as variables.


Repeat the process using the same variable values and the other pair of coefficient values to calculate a new constant term, *[tex \LARGE \gamma_2].  Then write your second equation.


Write back and tell me what you came up with for a system of equations and we can discuss several possible strategies for solving the system.


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