Find the value of $k$ for which the following system of equations has no solution:
$2 x - k y + 3 = 0$
$3 x + 2 y - 1 = 0$

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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.

$\Rightarrow \frac{2}{3} = \frac{- k}{2}$

$\Rightarrow k = \frac{- 4}{3}$

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