solving augmented matrices?

Question

solve using augmented matrices:
x + 2y - z = 3
3x + y - 2z = -6
x + y + z = 1

i've been trying to do this for almost twenty minutes and i'm dying :[
someone please help, and show your work? teehee

Answer 1

1 2 -1 3
3 1 -2 -6
1 1 1 1

Subtract 3 times first row from second row; subtract first row from third row:

1 2 -1 3
0 -5 1 -15
0 -1 2 -2

Divide 2nd row by (-5):

1 2 -1 3
0 1 -1/5 3
0 -1 2 -2

Subtract 2 times second row from first row; add second row to third row:

1 0 -3/5 -3
0 1 -1/5 3
0 0 9/5 1

Multiply third row by 5/9:

1 0 -3/5 -3
0 1 -1/5 3
0 0 1 5/9

Add 3/5 times third row to first row; add 1/5 times third row to second row:

1 0 0 -8/3
0 1 0 28/9
0 0 1 5/9