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

[1 mark]

One

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Infinite

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Two

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Zero

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Solution

The correct option is B Infinite
$a_{1} = 3, b_{1} = - 9, a n d c_{1} = 10 a_{2} = 9, b_{2} = 27, a n d c_{2} = 30$
$\frac{a_{1}}{a_{2}} = \frac{3}{9}, \frac{b_{1}}{b_{2}} = \frac{- 9}{27}, \frac{c_{1}}{c_{2}} = \frac{10}{30} \Rightarrow \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = \frac{1}{3}$

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

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