The lines represented by the equations $3 x + 5 y = 7 a n d 2 p x + 3 y = 1$ , are intersecting at a unique point for all values of p except $p = \frac{9}{10}$
Mention the answer as 1 if true else 0 if false

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Solution

Given $3 x + 5 y = 7 ⟶ (1)$
$2 p x + 3 y = 1 ⟶ (2)$
For equation to have unique solution, then,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
here,
$\frac{a_{1}}{a_{2}} = \frac{3}{2 p}$
$\frac{b_{1}}{b_{2}} = \frac{5}{3}$
$\frac{3}{2 p} \neq \frac{5}{3}$
$⟹ p \neq \frac{a}{10}$
For all values of $p$ except $\frac{9}{10}$ , the given lines represents intersecting lines.

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