The value of $k$ , for which the system of equation $k x + 2 y = 5$ , $3 x + y = 1$ has no solution, is

5

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\frac{2}{3}

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6

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\frac{3}{2}

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Solution

The correct option is A $6$
The equations are
$k x + 2 y = 5$ ....(1)
$3 x + y = 1$ ....(2)
From (1), we have
$y = - \frac{k x}{2} + \frac{5}{2}$
$∴$ slope $m_{1} = - \frac{k}{2}$
From (2), we have
$y = - 3 x + 1$
$∴$ slope $= m_{2} = - 3$
If the system has infinite number of solution, then
$m_{1} = m_{2}$
$\Rightarrow - \frac{k}{2} = - 3$
$\Rightarrow k = 6$

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