Find the value of $p$ for which the system
$2 x + p y = 1$
$3 x - 5 y = 7$
will have a unique solution

p = - \frac{10}{3}

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p = 7

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p \neq - \frac{10}{3}

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p \geq - \frac{10}{3}

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Solution

The correct option is C $p \neq - \frac{10}{3}$
To have an unique solution, the lines should not be parallel to each other. This means their slopes are not equal
$=> - \frac{2}{p} \neq - \frac{3}{5}$
$=> p \neq - \frac{10}{3}$

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