The system of equations $x + 2 y = 3$ and $3 x + 6 y = 9$ has

Unique solution

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No solution

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Infinitely many solutions

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Finite number of solutions

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Solution

The correct option is C Infinitely many solutions
Given equations are $x + 2 y = 3$ and $3 x + 6 y = 9$
$\frac{a_{1}}{a_{2}} = \frac{1}{3}; \frac{b_{1}}{b_{2}} = \frac{2}{6} = \frac{1}{3}, \frac{c_{1}}{c_{2}} = \frac{3}{9} = \frac{1}{3}$
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
Thus it has infinitely many solutions.

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