SOLUTION: I am having a really hard time understanding the Gauss-Jordan Method. I have reviewed everything I could possibly find on this subject and it seems like there is no formal way to

Question 34777: I am having a really hard time understanding the Gauss-Jordan Method. I have reviewed everything I could possibly find on this subject and it seems like there is no formal way to do this. I need a method to the madness? Please help if you can...
Use the Gauss-Jordan Mathod to solve these systems of linear equations.
Problem #1:
x+y+z=5
y+z=1
2z=4

Problem #2:
x+y=1
2x+3y=0
Your explanations of how to understand this method is greatly appreciated.
Thanks!
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
CREATING A MATRIX WE GET
1 1 1

0 1 1 OR1(2-0)-1(0-0)+1(0-0)OR 1*2-1*0+1*0 OR 2-0=0 OR 2 IS THE DENOMINATOR

0 0 2
FOR X WE GET
5 1 1
1 1 1 OR 5(2-0)-1(2-4)+1(0-4) OR 10+2-4 OR 8 DIV BY 2 WE GET 8/2=4 FOR X
4 0 2
FOR Y WE GET
1 5 1
0 1 1 OR 1(2-4)-5(0)+1(0)OR -2-5*0+1*0 OR -2 DIV BY 2 WE GET 2/-2=-1 FOR Y
0 4 2
FOR Z WE GET
1 1 5
0 1 1 OR 1(4-0)-1(0)+5(0) OR 4-0+0 OR 4 DIV BY 2 WE GET 2 FOR Z
0 0 4
THUS X=4, Y=-1 & Z=2

X+Y=1 & 2X+3Y=0 THEN X=1-Y SUBSTITUTING 1-Y FOR X IN EQUATION TWO WE GET
2(1-Y)+3Y=0 OR 2-2Y+3Y=0 OR 2+Y=0 OR Y=-2 THEN X=1-(-2) OR X=3

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