After solving a matrix using Gauss-Jordan Reduction, there's a row of zeroes. How do I write the final answer?

Question

I solved the following matrix

$\begin{bmatrix}1 & 2 & -1 & | & 3\\2 & 4 & -2 & | & 6\\3 & 6 & 2 & | & -1\end{bmatrix}$

and got

$\begin{bmatrix}1 & 2 & 0 & | & 1\\0 & 0 & 1 & | & -2\\0 & 0 & 0 & | & 0\end{bmatrix}$

therefore my final answer would be:

x =1 - 2y

z = -2

how do I write the "y" part?

Answer 1

The solution is correct as is, but a better way to present it would be:

$x=1-2t$

$y=t$

$z=-2$

where $t\in\mathbb R$.