The value of k for which the following system of linear equations represent coincident lines is
2x + 9y = k; 6x + 27y = 5

\frac{3}{5}

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\frac{2}{3}

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\frac{5}{3}

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\frac{6}{5}

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Solution

The correct option is C $\frac{5}{3}$
Given: 2x + 9y = k; 6x + 27y = 5
Let $a_{1} = 2$ , $b_{1} = 9$ , $c_{1} = k$ , and $a_{2} = 6$ , $b_{2} = 27$ , $c_{2} = 5$ .

For the lines to be coincident,
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} s = \frac{2}{6} = \frac{9}{27} = \frac{k}{5} s = \frac{2}{6} = \frac{k}{5} s = \frac{5}{3}$
Hence, the correct answer is option (3).

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