Question

I posted this question earlier but had a typo, can you take another look?

{ 1/3x + 3/4 y - 2/3 z = -8
x + 1/2 y - 1/3z = 18
1/6 x - 1/8 y - z = -24


a. (-6, 8, -24)
b. (-6, -8, -24)
c. (0, 8, -24)
d. (6, 8, 24)
e. (6, -8, 24)

Answer 1

I don't get with reduction any of those.

I get (-26,8/3,28)
http://matrix.reshish.com/gauss-jordanElimination.php

Answer 2

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Gauss-Jordan Elimination
Cramer's Rule
Inverse Matrix Method
Matrix Rank
Determinant
Inverse Matrix
Matrix Power
Matrix Transpose
Matrix Multiplication
Matrix Addition/Subtraction

Result of solution using Gauss-Jordan elimination
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Your matrix
№ X1 X2 X3 b
1 1/3 3/4 -2/3 -8
2 1 1/2 -1/3 18
3 1/6 -1/8 -1 -24

Find the pivot in the 1st column and swap the 2nd and the 1st rows
№ X1 X2 X3 b
1 1 1/2 -1/3 18
2 1/3 3/4 -2/3 -8
3 1/6 -1/8 -1 -24

Eliminate the 1st column
№ X1 X2 X3 b
1 1 1/2 -1/3 18
2 0 7/12 -5/9 -14
3 0 -5/24 -17/18 -27

Make the pivot in the 2nd column by dividing the 2nd row by 7/12
№ X1 X2 X3 b
1 1 1/2 -1/3 18
2 0 1 -20/21 -24
3 0 -5/24 -17/18 -27

Eliminate the 2nd column
№ X1 X2 X3 b
1 1 0 1/7 30
2 0 1 -20/21 -24
3 0 0 -8/7 -32

Make the pivot in the 3rd column by dividing the 3rd row by -8/7
№ X1 X2 X3 b
1 1 0 1/7 30
2 0 1 -20/21 -24
3 0 0 1 28

Eliminate the 3rd column
№ X1 X2 X3 b
1 1 0 0 26
2 0 1 0 8/3
3 0 0 1 28

Solution set:

x1 = 26
x2 = 8/3
x3 = 28
Computation time: 0.277 sec.
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Answer 3

Start with the url below and fix your typos till you get one of your choices:

http://www.wolframalpha.com/input/?i=solve+1%2F3x+%2B+3%2F4+y+-+2%2F3+z+%3D+-8,+x+%2B+1%2F2+y+-+1%2F3z+%3D+18,+1%2F6+x+-+1%2F8+y+-+z+%3D+-24