SOLUTION: 4x-4y+4z=-4 4x+y-2z=5 -3x-3y-4z=-16

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Question 1069956: 4x-4y+4z=-4
4x+y-2z=5
-3x-3y-4z=-16
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4x-4y+4z=-4
4x+y-2z=5
-3x-3y-4z=-16
---------------
x -y+ z=-1 1st eqn divided by 4
4x+y-2z=5
-3x-3y-4z=-16
------------
x -y+ z=-1 1st eqn divided by 4
4x+y-2z =5
---------------------- Add
5x - z = 4 Eqn A
---
12x+3y-6z= 15 2nd eqn times 3
-3x-3y-4z=-16
----------------------- Add
9x - 10z = -1 Eqn B
50x -10z = 40 Eqn A times 10
----------------------------- Subtract
-41x = -41
x = 1
===========
5x - z = 4 Eqn A
5 - z = 5
z = 1
===========
x -y+ z=-1
1 - y + 1 = -1
y = 3
--> (1,3,1)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Using Cramer's rule,
A=%28matrix%283%2C3%2C%0D%0A4%2C-4%2C4%2C%0D%0A4%2C1%2C-2%2C%0D%0A-3%2C-3%2C-4%29%29
abs%28A%29=-164
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A%5Bx%5D=%28matrix%283%2C3%2C%0D%0A4%2C-4%2C4%2C%0D%0A5%2C1%2C-2%2C%0D%0A-16%2C-3%2C-4%29%29
abs%28A%5Bx%5D%29=-164
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A%5By%5D=%28matrix%283%2C3%2C%0D%0A4%2C4%2C4%2C%0D%0A4%2C5%2C-2%2C%0D%0A-3%2C-16%2C-4%29%29
abs%28A%5By%5D%29=-492
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A%5Bz%5D=%28matrix%283%2C3%2C%0D%0A4%2C-4%2C4%2C%0D%0A4%2C1%2C5%2C%0D%0A-3%2C-3%2C-16%29%29
abs%28A%5Bz%5D%29=-164
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x=abs%28A%5Bx%5D%29%2Fabs%28A%29=-164%2F-164=1
y=abs%28A%5By%5D%29%2Fabs%28A%29=-492%2F-164=3
z=abs%28A%5Bz%5D%29%2Fabs%28A%29=-164%2F-164=1