Solve the system by Gauss - Jordan elimination.

{ 1/3 x + 3/4 y - 2/3 z = -8 x + 1/2 y + 1/3 z = 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)

Argghhh, hard to read, besides, you appear to have a typo near the end

1/6 x = 1/8 y - z = -24 -----> 1/6 x + 1/8 y - z = -24

did you mean:
1/3 x + 3/4 y - 2/3 z = -8
x + 1/2 y + 1/3 z = 18
1/6 x + 1/8 y - z = -24 ??

if so , I would clean them up first,
1/3 x + 3/4 y - 2/3 z = -8
times 12
4x + 9y - 6z = 96

x + 1/2 y + 1/3 z = 18
times 6
6x + 3y + 2z = 108

etc.

could you do it now?

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

To solve the system of equations using Gauss-Jordan elimination, we will transform the system into row-echelon form, and then into reduced row-echelon form.

Step 1: Write the augmented matrix of the system:
```
1/3 3/4 -2/3 | -8
1 1/2 1/3 | 18
1/6 -1 1/8 | -24
```

Step 2: Convert the first element of the matrix (which is 1/3) to be the leading coefficient by multiplying the entire row by 3:
```
1 1.5 -1 | -24
1 1/2 1/3 | 18
1/6 -1 1/8 | -24
```

Step 3: Use row operations to eliminate the first element in the second and third rows:
- Multiply the first row by -1 and add it to the second row:
```
1 1.5 -1 | -24
0 -1/2 2/3 | 42
1/6 -1 1/8 | -24
```
- Multiply the first row by -1/6 and add it to the third row:
```
1 1.5 -1 | -24
0 -1/2 2/3 | 42
0 -1.5 1.1667 | 0
```

Step 4: Convert the second element of the matrix (which is -1/2) to be the leading coefficient in the second row by multiplying the entire row by -2:
```
1 1.5 -1 | -24
0 1 -4/3 | -84
0 -1.5 1.1667 | 0
```

Step 5: Eliminate the second element in the first and third rows:
- Multiply the second row by -1.5 and add it to the first row:
```
1 0 -5/2 | 60
0 1 -4/3 | -84
0 -1.5 1.1667 | 0
```
- Multiply the second row by 1.5 and add it to the third row:
```
1 0 -5/2 | 60
0 1 -4/3 | -84
0 0 -4.5 | -126
```

Step 6: Convert the third element of the matrix (which is -4.5) to be the leading coefficient in the third row by multiplying the entire row by -2/9:
```
1 0 -5/2 | 60
0 1 -4/3 | -84
0 0 1 | 28
```

Step 7: Eliminate the third element in the first and second rows:
- Multiply the third row by 5/2 and add it to the first row:
```
1 0 0 | 32
0 1 -4/3 | -84
0 0 1 | 28
```
- Multiply the third row by 4/3 and add it to the second row:
```
1 0 0 | 32
0 1 0 | -56
0 0 1 | 28
```

The system is now in reduced row-echelon form, and we can read off the solution directly from the matrix. The solution is (32, -56, 28).

Therefore, the answer is not listed among the options provided.