Per this video at this moment, he says we can see the solution to this equation is $\begin{bmatrix} -1\\ 1 \end{bmatrix}$ (yellow line). Why?
Since $\begin{bmatrix} 1 & 1\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y\end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} $, wouldn't it give $x+y=0$ when solving by REFF as we ignore bottom row, resulting in..
$x = 1$ & $y = 1$ when, $x+y=0$?