The value of k, for which the system of equations 3x – ky – 20 = 0 and 6x – 10y + 40 = 0 has no solution,

System of equations

$a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ will have no solution if

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

$herefore frac{3}{6}=frac{-k}{-10} eq frac{-20}{40}$

$Rightarrow frac{1}{2}=frac{k}{10} Rightarrow k=frac{10}{2}=5$