Find the value of $k$ for which the given system of equation has no solution.
$k x + 2 y - 1 = 0$
$5 x - 3 y + 2 = 0$

k = - \frac{1}{5}

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k = - \frac{10}{3}

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k = \frac{9}{5}

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k = \frac{6}{5}

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Solution

The correct option is B $k = - \frac{10}{3}$
The equations are
$\Rightarrow k x + 2 y - 1 = 0$
$\Rightarrow a_{1} = k, b_{1} = 2, c_{1} = - 1$
$\Rightarrow 5 x - 3 y + 2 = 0$
$\Rightarrow a_{2} = 5, b_{2} = - 3, c_{2} = 2$

The given system of equations has no solution
$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

$\Rightarrow \frac{k}{5} = \frac{2}{- 3} \Rightarrow k = - \frac{10}{3}$

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