For what value of k, the pair of linear equations $3 x + k y = 9$ and $6 x + 4 y = 18$ has infinitely many solutions?

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Solution

The correct option is D
2

Given equations gives infinitely many solutions if,
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

The given linear equations are:
$3 x + k y = 9; 6 x + 4 y = 18.$
$\Rightarrow a_{1} = 3, b_{1} = k, c_{1} = - 9$ and $a_{2} = 6, b_{2} = 4, c_{2} = - 18$

$\Rightarrow \frac{3}{6} = \frac{k}{4} = \frac{- 9}{- 18}$

$\Rightarrow \frac{1}{2} = \frac{k}{4}$

$\Rightarrow k = 2$

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