Find the value of $k$ for which the following system of equations has no solution:
$x + 2 y = 0$
$2 x + k y = 5$

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Solution

For the system of equations to have no solution, the lines must be parallel.

$\Rightarrow$ The ratio of ' $x$ ' and ' $y$ ' coefficients must be equal.

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

$\Rightarrow k = 4$

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