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

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Solution

The correct option is D
2

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

Given equations gives infinitely many solutions,
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{3}{6} = \frac{k}{4} = \frac{9}{18}$
$\Rightarrow \frac{1}{2} = \frac{k}{4}$
$\Rightarrow k = 2$

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