The system of equations
$x+ky = 0$
$3x+5y = 0$
has infinitely many solutions, then $k$ is equal to
Answer & explanation
Correct answer: option 2
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 $\frac{5}{3}$.