Question 225488
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Given the system:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\{1:\ \ \,x\ -\ 6y\ =\ 7\cr2:\ 2x\ -\ 6y\ =\ 2\right]


Multiply Equation 1: by -1:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left\{1:\ -x\ +\ 6y\ =\ -7\cr2:\ 2x\ -\ 6y\ =\ \ \,2\right]


Notice that the coefficients on the *[tex \Large y] terms are additive inverses.  Add the like terms of the two equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -x\ +\ 2x\ +6y\ -6y\ =\ -7\ + 2]


The *[tex \Large y]-terms have been eliminated, hence the name of the method.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = -5]


From here you can either take the value of *[tex \Large x] that we just derived and substitute it into either of the original equations then solve for *[tex \Large y], or you could multiply the original Equation 1: by -2 and add the two equations, thus eliminating the *[tex \Large x] terms giving you a single linear equation in *[tex \Large y].


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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