For what value of k, the following system of equations will represent the coincident lines?

GIVEN: 

$x+2 y+7=0$

$2 x+k y+14=0$

To find: To determine for what value of k the system of equation will represents coincident lines

We know that the system of equations

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

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

For the system of equation to represent coincident lines we have the following relation

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

Here,

$\frac{1}{2}=\frac{2}{k}=\frac{7}{14}$

$\frac{1}{2}=\frac{2}{k} \quad$ and $\quad \frac{2}{k}=\frac{7}{14}$

$k=4 \quad$ and $\quad k=4$

Hence for $k=4$ the system of equation represents coincident lines