Question 234161
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3b\ -\ c\ =\ 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2a\ -\ b\ -\ 2c\ =\ -5]


I don't know how you do it.  But I would use the substitution method on this one.


Solve the 2nd equation for *[tex \Large c]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ =\ 3b\ -\ 4]


Substitute this expression for *[tex \Large c] into the first equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ (3b-4)\ =\ 3]


and then simplify:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ 4b\ =\ 7]


Solve this one for *[tex \Large a]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ 7\ - 4b]


Substitute this expression for *[tex \Large a] and the previously derived expression for *[tex \Large c] into the third equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2(7-4b)\ -\ b\ -\ 2(3b-4)\ =\ -5].


And then solve for *[tex \Large b]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 14\ -\ 8b\ -\ b\ -\ 6b\ +\ 8\ =\ -5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -15b\ =\ -27]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ \frac{9}{5}]


Substitute this value for *[tex \Large b] the derived expression for *[tex \Large c] and solve for *[tex \Large c].  Substitute the values for *[tex \Large b] and *[tex \Large c] into the original first equation and solve for *[tex \Large a].  The last couple of steps are left as an exercise for the student.


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