Linear Algebra Row Reduction: Solving a System of Equations with Row Operations

[SMA_01]

Linear Algebra Row Reduction?

Homework Statement

This question is frustrating me, and I might be missing the obvious, I tend to make algebraic mistakes, but I don't know what I'm doing wrong here!

I'm trying to solve this system using row reduction:

x-5y+4z=-3
2x-7y+3z=-2
-2x+y+7z=-1

Note this does not have to be in reduced echelon form, just regular echelon form.

The Attempt at a Solution

Okay so I started like this:
Note: "l" indicated the bar representing "=" sign
1 -5 4 l -3
2 -7 3 l -2 --> I then used -2(2nd row)+1st row
-2 1 7 l -1 --> And 2(1st row)+ 3rd row

To get:

1 -5 4 l -3
0 3 -5 l 4
0 -9 15 l -7
I'm trying to remove the -9 in the third row but can't seem to do it without the 15 becoming zero.

Any help please?

 

[estro]

HINT: Some problems have more then 1 solution, some don't have any. [what is yours case?]