ive tried it a bunch of times ending up with the same thing, the only thing left is to have someone point out where i screwed up. The answer is (9,9,6) but i want to understand how to get there

Ok so heres the problem

1) 6x-9y-z=-33

2)x-3y+4x=6

3)5x+y+z=60

I start with 1 and 3 to form equation 4

1) 6x-9y-z=-33

3)5x+y+z=60

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4)11x -8y = 27 (cancel z, add)

Then I use equations 1 and 2 to form equation 5

1) 6x-9y-z=-33

2)x-3y+4x=6

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5) 25x - 39y = -126 (I multiply eq1 by 4)

4) 11x -8y = 27

5) 25x - 39y = -126

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-429x = -1053

200x = 1008

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-229x = -45

x=-45/-229

I dont know if im just making a bone headed mistake over and over, or if theres something im straight up forgetting. but this is as far as i get, knowing that x must be 9.