The value of k for which the system of equations 3x + 5y = 0

The given system of equations are,

$3 x+5 y=0$

$k x+10 y=0$

Here, $a_{1}=3, a_{2}=k, b_{1}=5, b_{2}=10$

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b} \neq 0$

$\frac{3}{k}=\frac{5}{10} \neq 0$

By cross multiply we get

$30=5 k$

$\frac{30}{5}=k$

$6=k$

Therefore the value of k is 6,

Hence, the correct choice is c.