Set up:

Move the 2nd row to the top row. You'll see why.

Take the 2nd row: subtract 7x the top row from each entry.

Divide all entries in 2nd row by -15.

Third row: subtract 2x the top row from each entry.

Divide each entry in the 3rd row by -3.

Third row: subtract 3/2x of the 2nd row.

Multiply the entries in the 3rd row by -2.

This can be solved by back substitution, now. If you want to practice your row skills, find the answer by back substitution, then check yourself: find the answer directly by reducing it to this form:

You might also do the steps above yourself and check my work. Maybe I tossed in a monkey wrench somewhere along the way ...?