SOLUTION: SOLVE THE SYSTEM USING THE GAUSS-JORDAN METHOD PROBLEM: x-2y= -1 2x+y= -7 PLEASE HELP SOLVE.. I UNDERSTAND THE FORMULA COMPLETLY AND HOW IT SHOULD COME OUT TO LOOK LIKE

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Question 136221: SOLVE THE SYSTEM USING THE GAUSS-JORDAN METHOD
PROBLEM: x-2y= -1
2x+y= -7
PLEASE HELP SOLVE.. I UNDERSTAND THE FORMULA COMPLETLY AND HOW IT SHOULD COME OUT TO LOOK LIKE [ 1 0.. AND BENEATH THAT 0 1..] YET JUST THE PROCESS OF SOLVING IT LOSES ME.. I DO UNDERSTAND HOW TO SET IT UP THOUGH
[ 1 -2..-1]
[2 1..-7] THANK YOU FOR YOUR TIME... lj23kfuller@yahoo.com
Answer by dolly(163) (Show Source):
You can put this solution on YOUR website!
I'll help you
You got the matrix [1 2 -1]
[2 1 -7]
Now we perform row operations basically to make the elements below and above the principal diagonal as 0
Consider R2 - 2 R1
So the matrix becomes [1 2 -1]
[0 -3 -5]
Now the element below the diagonal became 0
To get the elemnts along the diagonal as 1,
we divide the R2 by -3
==> [1 2 -1]
[0 1 -5/-3]
= [1 2 -1]
[0 1 5/3]
Now to make the element above the diagonal 0, perform
R1 - 2 R2
==> [1 0 -1-10/3]
[0 1 5/3]
==> [1 0 -13/3]
[0 1 5/3]
This represents the original equation
Thus we get x = -13/3 and y = 5/3
These satisfy the given equation.
Hope it is clear
Good luck!!!
Dolly