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

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Solution

The correct option is C 4
Given sysytem of equations are $x + 2 y + 7 = 0,$ and $2 x + k y + 14 = 0$

Condition for coincident lines is

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

$a_{1} = 1, a_{2} = 2, b_{1} = 2, b_{2} = k$

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

$\Rightarrow k = 4$

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