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I know that we are to end up with a matrices in the form of
1 ? ? ?
0 1 ? ?
0 0 1 ?

@LadyInkblot have you converted the system to a matrix yet?

Yes.
It starts out as a matrix of
1 -5 4 -3
2 -7 3 -2
-2 1 7 -1

How far have you gotten with reducing the matrix?

I don't know if this is correct, but so far I have
1 -5 4 -3
0 3 -5 4
0 -10 15 -7

I preformed (I believe) 2R1 + R3 and -2R1 - R2

I do not know how to proceed, which is why I came here for help ^_^;

May I suggest a different approach?

Of course!

Just row 2 + row 3? not multiplying anything?

Yes, actually do
R2 + R3, then -2R1 + R2

okay. I'll get back to you in a minute then with my answer...

Okay, so I got
1 -5 4 -3
0 3 -5 0
0 6 -4 -4

But then I'll still have to get rid of the 6 in the third row... so what about 2R2 + r3?

You should double check your work for those 2 operations.

okay, what's wrong with it?

Okay, I tried again and got something different
1 -5 4 -3
0 3 -5 -8
0 -6 10 -3

The 1st and 3rd row are correct. The second row has a mistake with the -8

Ah. Would it be a 4?

Yes

1 -5 4 -3
0 3 -5 4
0 0 0 5

You're jumping too far ahead.

Please post just the first two operations.

1 -5 4 -3
0 3 -5 4
0 -6 10 -3

Yes. What does that mean, an invalid row.
1 -5 4 -3
0 3 -5 4
0 0 0 5

Okay. So what does that mean for the answer to the problem then. Just that the solution is invalid?

It means the system cannot be solved and therefore has no solution.

Okay, that makes sense.
Thank you!

You're welcome. Great work on your problem.

Thank you!