SOLUTION: I need some help with Gaussian elimination for equation systems: x+y-z=3 -x+2y+5z=-17 3x+5y+4z=-22 x= y= z=

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Question 321336: I need some help with Gaussian elimination for equation systems:
x+y-z=3
-x+2y+5z=-17
3x+5y+4z=-22
x= y= z=
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
use the -z in the 1st eqn to eliminate the z terms in the 2nd and 3rd eqns

multiply 1st by 5 and add to second ___ (A) ___ 4x + 7y = -2

multiply 1st by 4 and add to 3rd ___ (B) ___ 7x + 9y = -10

multiply (A) by -7 and add to 4 times (B) ___ -13y = -26 ___ y = 2

substitute to find x ___ 4x + 7(2) = -2 ___ x = -4

substitute to find z ___ (-4) + (2) - z = 3 ___ z = -5