For what values of $m$ , the pair of equations $3 x + m y = 10$ and $9 x + 12 y = 30$ have a unique solution.

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Solution

Given equations,
$3 x + m y = 10$ and $9 x + 12 y = 30$
Second equation can be reduced to $3 x + 4 y = 10$ . So both the lines are parallel to each other for real values of $m$ .
Therefore there will be no value of $m$ for them to have unique solution.

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