Hi I really need help!

I did the questions but something went wrong in my working, can someone please show me how to derive the answer with row reduction?! I really am confused when to express my answer in parametric equations!

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After Row reduction I got

\begin{bmatrix} x \\y \\z \end{bmatrix}[/tex] =

For Row two, I took row 2 - 2 times row 1

FOr Row 3, I took row 3 minus Row 1

So, since I did not get all zeros ir at least three zeros in the bottom entries, I resorted to represent unique solutions in parametric equations, I got y=1-3t, z=t and x=3+t..however, the answer is in whole numbers for each x, y and z. And when I pressed the matrix into the calculator to solve for x, y and z, I got whole numbers too..

How do I know that I am to use parametric equations to solve? And how do I get the whole numbers in this case?

Thank you so much, your help is much appreciated!