Find the value of k for which each of the following system of equations have infinitely many solutions :

GIVEN: 

$8 x+5 y=9$

$k x+10 y=18$

To find: To determine for what value of k the system of equation has infinitely many solutions 

We know that the system of equations

$a_{1} x+b_{1} y=c_{1}$

$a_{2} x+b_{2} y=c_{2}$

For infinitely many solution 

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Here,

$\frac{8}{k}=\frac{5}{10}=\frac{9}{18}$

$\frac{8}{k}=\frac{5}{10}$

$k=\frac{8 \times 10}{5}$

$k=8 \times 2$

$k=16$

Hence for $k=16$ the system of equation have infinitely many solutions