Expert: Paul Klarreich - 9/25/2008

Question
2x-y+2Z=10
4X+2Y-5Z=10
X-3Y+5Z=8

Answer
Questioner:   Reuben Feagin
Category:  Advanced Math
Private:  No
 
Subject:  solving systems of three variables
Question:  
2x-y+2Z=10
4X+2Y-5Z=10
X-3Y+5Z=8
............................................
Hi, Reuben,

It isn't clear what your problem is.  So I will get you started and let you finish up.

You start by taking two of the equations and eliminating one of the variables.  For example:

2x -  y + 2Z = 10  (A)
4X + 2Y - 5Z = 10  (B)
X - 3Y + 5Z = 8   (C)

Use A and B to eliminate y:

4x - 2y + 4Z = 20  (2A)
4X + 2Y - 5Z = 10  (B)
------------------------ Add
8x      -  Z = 30  (D)

Next take two of the equations and eliminate the SAME variable.  For example:

Use A and C to eliminate y:
-6x + 3y - 6Z = -30  (-3A)
 X - 3Y + 5Z =   8   (C)
-------------------------- Add
- 5x     - z = -22  (E)

Now use these two equations in two variables to solve for x,z.  Subst back into A,B, or C to find y.

Finito.