The system of equations
$x+ky = 0$
$3x+5y = 0$
has infinitely many solutions, then $k$ is equal to

$\frac{5}{3}$

The correct answer is Option (2) → $\frac{5}{3}$ **

For the system to have infinitely many solutions, the two equations must be proportional.

Given:

$x + ky = 0$

$3x + 5y = 0$

For proportionality:

$\frac{1}{3} = \frac{k}{5}$

Cross-multiply:

$5 = 3k$

$k = \frac{5}{3}$

The value of $k$ is $\frac{5}{3}$.