SOLUTION: I have been working on this for over an hour. My numbers seem too high to be real. Set up an augmented matrix and use the Gaussian elimination method to solve each system. 5

Question 866215: I have been working on this for over an hour. My numbers seem too high to be real.
Set up an augmented matrix and use the Gaussian elimination method to solve each system.
5x-y+z=17
2x+3y-z=-9
x-4y+3z=26
I got x=14897/4505, y=3767/901, and z=-60/53
I have no clue where I went wrong. But I don't think that these are the correct answers. Any help is appreciated please and thank you.
Thank you in advance for the help.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x = 2, y = -3, z = 4
Divide row1 by 5
1 -1/5 1/5 17/5
2 3 -1 -9
1 -4 3 26
Add (-2 * row1) to row2
1 -1/5 1/5 17/5
0 17/5 -7/5 -79/5
1 -4 3 26
Add (-1 * row1) to row3
1 -1/5 1/5 17/5
0 17/5 -7/5 -79/5
0 -19/5 14/5 113/5
Divide row2 by 17/5
1 -1/5 1/5 17/5
0 1 -7/17 -79/17
0 -19/5 14/5 113/5
Add (19/5 * row2) to row3
1 -1/5 1/5 17/5
0 1 -7/17 -79/17
0 0 21/17 84/17
Divide row3 by 21/17
1 -1/5 1/5 17/5
0 1 -7/17 -79/17
0 0 1 4
Add (7/17 * row3) to row2
1 -1/5 1/5 17/5
0 1 0 -3
0 0 1 4
Add (-1/5 * row3) to row1
1 -1/5 0 13/5
0 1 0 -3
0 0 1 4
Add (1/5 * row2) to row1
1 0 0 2
0 1 0 -3
0 0 1 4

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