SOLUTION: Use left to right elimination method to solve the system x-3y-z=0 x-2y+z=8 2x-6y+z=6

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Question 261294: Use left to right elimination method to solve the system
x-3y-z=0
x-2y+z=8
2x-6y+z=6
Answer by CharlesG2(834) About Me  (Show Source):
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Use left to right elimination method to solve the system
x-3y-z=0
x-2y+z=8
2x-6y+z=6
x - 3y - z = 0 (multiply by -2 and add to the 3rd)
x - 2y + z = 8
2x - 6y + z = 6
-2x + 6y + 2z = 0
x - 2y + z = 8
0x + 0y + 3z = 6
3z=6 --> z=2
-2x + 6y + 4 = 0 --> -2x + 6y = -4
x - 2y + 2 = 8 --> x - 2y = 6 (multiply by 2)
-2x + 6y = -4
2x - 4y = 12 (add 1st to 2nd)
-2x + 6y = -4
0x + 2y = 8
2y=8 --> y=4
-2x + 6*4 = -4
-2x + 24 = -4
-2x = -28
x=14
check: x-3y-z=0 --> 14 - 3*4 - 2 = 14 - 12 - 2 = 14 - 14 = 0
x-2y+z=8 --> 14 - 2*4 + 2 = 14 - 8 + 2 = 14 - 6 = 8
2x-6y+z=6 --> 2*14 - 6*4 + 2 = 28 - 24 + 2 = 4 + 2 = 6