Which of the following is correct to the line  $5x+y+3z=0$ and $3x-y+z+1=0$

The given planes are  $5x+y+3z=0$ and $3x-y+z+1=0$

Suppose that the direction ratios of line of intersection of the above two planes is $⟨a,b,c⟩$

Hence, $3a-b+c=0,5a+b+3c=0$$\Rightarrow \frac{a}{1}=\frac{b}{1}=\frac{c}{-2}$

To get a point on the line, substitute $z=0$  in the plane equations and the solve for the other variables 

hence a point on the  line of intersection of planes is $P\left(-\frac{1}{8},\frac{5}{8},0\right)$

Therefore, the equation of the required line is $\frac{x+\frac{1}{8}}{1}=\frac{y-\frac{5}{8}}{1}=\frac{z}{-2}$