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