Can this triple SysEq have multiple solutions?

Question

A) $x+2y-z=6$ B) $2x-y+3z=-13$ C) $3z-2y+3z=-16$

I got $x=-1$ , $y=2$ , $z=-3$

But, then I also got $x=11$ , $y=27$ , $z=-32$ by combining and eliminating in a different order.

Is this possible?

Answer 1

$$11+2(27)-(-32)=11+54+32> 6$$

The second proposed solution is not a solution to the linear system.

While for a general linear systems of equations might have more than one solution, in this case, note that the determinant of the corresponding matrix is non-zero, the solution should be unique.

>> det([1 2 -1; 2 -1 3; 3 -2 3])

ans =

    10