If the system of linear equations \(x + y + 3z = 0\) \(x + 3y + k^{2}z = 0\) \(3x + y + 3z = 0\) has a non-zero solution…

If the system of linear equations

\(x + y + 3z = 0\)

\(x + 3y + k^{2}z = 0\)

\(3x + y + 3z = 0\)

has a non-zero solution \((x,y,z)\) for some \(k \in R\) , then \(x + \left( \frac{y}{z} \right)\) is equal to : -

[JEE Main 2020, 5 Sep (Shift 2)]