SOLUTION: I have been trying to get this problem right but am having no luck. It needs to be done using the Gauss-Jordan method. Can someobdy help. x + 3y - 6z = 7 2x

SOLUTION: I have been trying to get this problem right but am having no luck. It needs to be done using the Gauss-Jordan method. Can someobdy help. x + 3y - 6z = 7 2x - y + 2z = 0 x +

Question 208177: I have been trying to get this problem right but am having no luck. It needs to be done using the Gauss-Jordan method. Can someobdy help.
x + 3y - 6z = 7
2x - y + 2z = 0
x + y + 2z = -1
Any help would be appreciated.
Thanks.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x + 3y - 6z = 7
2x - y + 2z = 0
x + y + 2z = -1
----------------------------
Subtract 1st equation from the 3rd:
Subtract 2 times the 1st equation from the 2nd:
------------------------------------------------
x + 3y - 6z = 7
0 - 7y + 14z = -14
0 - 2y + 8z = -8
---------------------------
Divide thru the 3rd by -2 to get:
----------------------------------------
x + 3y - 6z = 7
0 - 7y + 14z = -14
0 + y - 4z = 4
--------------------------
Add 7 times the 3rd to the 2nd:
Subtract 3 times the 3rd from the 1st:
--------------------------------
x + 0 + 6z = -5
0 + 0 - 14z = 14
0 + y - 4z = 4
---------------------------------
Interchange the 2nd and the 3rd to get:
x + 0 + 6z = -5
0 + y - 4z = 4
0 + 0 - 14z = 14
----------------------------------
Divide thru the 3rd by -14 to get:
x + 0 + 6z = -5
0 + y - 4z = 4
0 + 0 + z = -1
------------------------
Add 4 times the 3rd to the 2nd:
Subtract 6times the 3 from the 1st:
---------------------------------------
x + 0 + 0 = 1
0 + y + 0 = 0
0 + 0 + z = -1
---------------------------
x = 1
y = 0
z = -1
==============
Cheers,
Stan H.

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