SOLUTION: how do u solve these linear systems by gauss elimination or any other method? x -5y +0z +10w= 27 5x -25y +10z -4w= -47 10x +2y -1z +4w= 36 2x +4y -2z +0w= 12

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Question 5154: how do u solve these linear systems by gauss elimination or any other method?
x -5y +0z +10w= 27
5x -25y +10z -4w= -47
10x +2y -1z +4w= 36
2x +4y -2z +0w= 12

Thank you very much I appreciate your help.
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
user Cramer's rule --> but that will involve you calculating 4x4 determinants, so you may decide to ignore that method :-)

Gaussian elimination... here goes :-(

re-arrnage the rows to move the zero further down and get the smallest number (the 14) in the correct place

divide second by 14 to get a 1

divide by 10 to get a 1

so, 13w = 39 --> w=3
z - 81/5 = -91/5 --> z = -2
y + 2/7 - 30/7 = -3 --> y = 1
x - 5 + 30 = 27 --> x = 2

THEN IMPORTANTLY, you need to put these 4 answers into each of the original 4 equations to check...check with the 4th one first --> if that works, then odds on you are correct.

PS i hate Gaussian Elimination!

jon