Solve the linear system with the given augmented matrix (the last column should have the dots before it but I'm not sure how to enter those)

First I subtracted the 2nd row from the 1st to get:

Then I subtracted 3 x row 1 from row 2 and 5 x row 1 from row 3 to get:

I subtracted row 3 from row 2 to get:

Since I have a row of 0 0 0 1, I believe there is no solution. Am I doing this wrong? or maybe missed a step?