For which value of $p$ does the equation $4 x + p y + 8 = 0$ and $2 x + 2 y + 2 = 0$ have unique solution?

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Solution

Solution:
$L_{1} : 4 x + p y + 8 = 0$
$L_{2} : 2 x + 2 y + 2 = 0$
For an unique solution,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
so, $\frac{4}{2} \neq \frac{p}{2}$
or, $p \neq 4$
Value of $p = R - {4}$

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