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Conditions for a system of linear equations to have infinite solutions

The value of ...

Question

The value of $k$ for which the system of equations $k x + 2 y = 5, 3 x + y = 1$ , 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 C $6$
$k x + 2 y = 5$
$\pm 6 x \pm 2 y = - 2 - --------------- -$
$(k - 6) x = 3$
System has no solution for $k = 6$ .

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