Question 588766
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Let *[tex \Large x] represent the 10s digit of the unknown number.  Let *[tex \Large y] represent the 1s digit.  The number can be represented by *[tex \Large 10x\ +\ y] and the number with the digits reversed can be represented by *[tex \Large 10y\ +\ x].


We are given that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 8]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (10x\ +\ y)\ -\ (10y\ +\ x)\ =\ 18]


Collect like terms and simplify the second equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9x -\ 9y\ =\ 18]


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


Leaving us with the 2X2 system:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 8]


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


Solve by elimination.


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