I am resolving the following matrix:

```
 1  2 1|1
-1  4 3|2
 2 -2 a|3

```

Where I have to find all the values of $a$ so that the system can have a unique solution. Doing elementary row operations I ended up with:

```
1 2  1 |1
0 1 2/3|1/3
0 0 2+a|4

```

Where I see that $a$=2. Using this for back substitution: $z$=1, $y$=-1/3 and $x$=-2/3 The problem is that this values does not satisfy the system (last equation of the original matrix)

Can someone explain the right procedure to find all the values of $a$?
What I am doing wrong?