Unknown in Gaussian Eliminations

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I saw an interesting while browsing the internet. Is there any expert that may explain the way to solve questions like this?

Questions

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Hint:

I would consider two cases:

Case $1$: $x_1 \neq 0$. what can you conclude since it is in RREF form.

Case $2$. $x_1 = 0$. I will further consider two cases, $x_2=0$ and $x_2 \neq 0$.

Overall idea is to consider cases and make conclusion from the RREF.