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How can I justify whether I'm able to apply the Gaussian elimination method to this system?

I'm currently practicing some Gaussian elimination questions for my discrete math topic, I came across this question and I need help. How can I justify whether I'm able to apply the Gaussian elimination method to this system?
Question:
~~> Consider the following system of linear equations.~~
>
~~> $$\begin{eqnarray*}a_{12}y + a_{13}z &=& b_1 \\\\~~
~~> a_{21}x + a_{23}z &=& b_2 \\\\~~
~~> a_{31}x + a_{32}y &=& b_3\end{eqnarray*}$$~~
>
> Can you apply Gaussian elimination to this system? Justify your answer.

Hey I'm currently practicing some Gaussian elimination questions for my discrete math topic, I came across this question and I need help. How can I justify whether I'm able to apply the Gaussian elimination method to this system? Thanks a bunch.
Question:
Consider the following system of linear equations.
$$
\begin{cases}
\alpha_{12}y + \alpha_{13}z=b_3\\\\
\\\\
\alpha_{21}x + \alpha_{23}z=b_2\\\\
\\\\
\alpha_{31}x + \alpha_{32}y=b_3
\end{cases}
$$
Can you apply Gaussian elimination to this system? Justify your answer.
BTW '$\alpha_{31}x$' is like a (row 3 column 1) multiplied by coefficient '$x$'.

equation system gaussian

linear-algebra equation system gaussian