essendoubleop

I have a 3x4 matrix and I need to put it in reduced row echelon form. I plugged it into the calculator and found the answer should be (10,2,3), but I can't figure out how I got the first number wrong. Here are each step I took:

5x + 9y - 7z = 47
4x - 3y + 2z = 40
9x + 8y - 3z = 97

{5 9 -7 47
4 -3 2 40
9 8 -3 97}

{1 12 -9 7
4 -3 2 40
9 8 -3 97}

{1 12 -9 7
0 -51 38 12
0 -100 78 34}

{1 0 3 (277/3)
0 -1 -1 -5
0 -100 78 34}

{1 0 3 (277/3)
0 1 1 5
0 0 178 534}

{1 0 0 (250/3)
0 1 1 5
0 0 178 534}

{1 0 0 (250/3)
0 1 0 2
0 0 1 3}

By my answer I get (250/3), 2, 3. I can't figure out what I did wrong.