For what value of k will the pair of equations $x + 2 y + 7 = 0, 2 x + k y + 14 = 0$ represent coincident lines?

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Solution

The correct option is C 4
Condition for coincident lines is

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

$x + 2 y + 7 = 0 a n d 2 x + k y + 14 = 0$

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

$\Rightarrow k = 4$

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