SOLUTION: I have tried this several different ways. I don't know how to do it. Please help. Solve for x,y,z 3x+2y-4z=-100 4x-3y+2z=80 5x-4y-z=-120

Question 72669: I have tried this several different ways. I don't know how to do it. Please help.
Solve for x,y,z
3x+2y-4z=-100
4x-3y+2z=80
5x-4y-z=-120
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve for x,y,z
:
Well one way, that does not involve matrix operations is multiple elimination:
:
Eq1: 3x+2y-4z=-100
Eq2: 4x-3y+2z=80
Eq3: 5x-4y-z=-120
:
Mult eq 2 by 2 and add it to eq1
3x + 2y - 4z = -100
8x - 6y + 4z = 160
----------------------- eliminates z
11x - 4y = 60
:
:
Mult eq3 by 2 and add it to eq 2:
4x - 3y + 2z = 80
10x - 8y - 2z = -240
------------------------eliminates z
14x - 11y = -160
:
Using these two equations, mult the 1st by 11 and the 2nd by 4
:
121x - 44y = 660
56x - 44y = -640
---------------------subtracting eliminates y, solving for x
65x = +1300
x = 1300/65
x = 20
:
Let's use 11x - 4y = 60 to find y, substitute 20 for x
11(20) - 4y = 60
220 - 4y = 60
-4y = 60 - 220
y = -160/-4
y = +40
:
I'm going to let you find z by substituting for x & y, in one of the original
equations. Then check all the solutions in one of the other original equations.

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