The number of solutions of the given pair of linear equations $3 x - 9 y = 10$ and $9 x - 27 y = 30$ is:

Infinite

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One

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Two

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Zero

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Solution

The correct option is A Infinite
Here, $a_{1} = 3, b_{1} = - 9, c_{1} = - 10$
and $a_{2} = 9, b_{2} = - 27, c_{2} = - 30$

$\frac{a_{1}}{a_{2}} = \frac{3}{9}, \frac{b_{1}}{b_{2}} = \frac{- 9}{- 27}, \frac{c_{1}}{c_{2}} = \frac{- 10}{- 30}$

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ = $\frac{1}{3}$

So, the given pair of straight lines have infinite solutions.

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