Question

Find four solutions of the equation 6x+3y=9.

Answer 1

Definitely \[x=\frac{ 3 }{ 2 }\] and \[y=0\] If looking for 4 solutions possibly also\[x=\frac{ 3 }{ 2}-\frac{ 1 }{ 2 }y\] and \[y=3-2x\]

Answer 2

I think that solution is:
\[\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}0 \\ 3\end{matrix}\right)+\xi \left(\begin{matrix}1 \\ -2\end{matrix}\right)\]
when \[\forall \xi \in \mathbb{R} \]