The equations $6 x - 9 y = 5$ and $5 x - 6 y = 3$ have

Unique solution

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No solution

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Two solutions

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Infinite solutions

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Solution

The correct option is B Unique solution
The given pair of linear equations is
$6 x - 9 y = 5; 5 x - 6 y = 3$
Here $a_{1} = 6, b_{1} = - 9, c_{1} = - 5$
and $a_{2} = 5, b_{2} = - 6, c_{2} = - 3$
$∴ \frac{a_{1}}{a_{2}} = \frac{6}{5}, \frac{b_{1}}{b_{2}} = \frac{- 9}{- 6} = \frac{3}{2}, \frac{c_{1}}{c_{2}} = \frac{- 5}{- 3}$
Hence $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Thus the lines represented by given pair of linear equations intersect and hence have a unique solution.

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