Expert: Paul Klarreich - 12/9/2008

Question
x-2y+3z=7
2x+y+2=4
-3x+2y-2z=-10

Answer
Questioner:   bunchie
Category:  Advanced Math
Private:  Yes
 
Subject:  solving system of equation with three variables
Question:  

x-2y+3z=7 (A)
2x+y+2z=4  (B)
-3x+2y-2z=-10  (C)
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Hi,Bunchie,

Note: Don't mark 'Private'. I change it anyway. If you don't want anyone on this site to see the question, send it somewhere else.
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Here is what you do:

Take two of your equations and find a combination that eliminates a variable.

I would take -2A + B, and eliminate x.

That gives:
5y - 4z = - 10

Take another two and eliminate the same variable.

Take 3A + C, and eliminate x.

-4y + 7z = 11


Now you have two equations in two variables.  I will assume you know what to do at that point.  (Hint; you are going to get FRACTIONS, assuming you entered the example correctly.  Sorry about that.)