For what value of k, the following system of equations has infinitely…

The correct answer is Option (2) → 6

Given system:

$x+2y=5$

$3x+ky=15$

For infinitely many solutions, the equations must be dependent:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Write in standard form:

$x+2y-5=0$

$3x+ky-15=0$

So

$\frac{1}{3}=\frac{2}{k}=\frac{-5}{-15}$

$\frac{1}{3}=\frac{2}{k}=\frac{1}{3}$

From $\frac{2}{k}=\frac{1}{3}$

$k=6$