The pair of linear equations $2 x + 5 y = k, k x + 15 y = 18$ has infinitely many solutions if

k = 3

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k = 6

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k = 9

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k = 18

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Solution

The correct option is B $k = 6$
The pair of linear equations
$2 x + 5 y = k$
and $k x + 15 y = 18$
Here, $a_{1} = 2, b_{1} = 5, c_{1} = - k$
and $a_{2} = k, b_{2} = 15, c_{2} = - 18$
The system of equation has infinitely many solutions if
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{2}{k} = \frac{5}{15} = \frac{- k}{- 18}$
$\Rightarrow \frac{2}{k} = \frac{1}{3} = \frac{k}{18}$
Taking,
$\frac{2}{k} = \frac{1}{3} \Rightarrow k = 6$
Taking,
$\frac{1}{3} = \frac{k}{18} \Rightarrow k = 6$
So, answer is $k = 6$

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