Find p for which given equation has unique solution $4x+py+8=0$ $2x+2y+2=0$

Given: $4x+py+8=0$ and $2x+2y+2=0$

To do: To find the value of $p$ if the pair of equations has a unique solution.

Two equations, 4x+py+8=0 and 2x+2y+2=0

As known the condition for a unique solution is :

$\frac{a_1}{a_2}\
eq\frac{b_1}{b_2}$

Here, $a_1 = 4,\ b_1 = p,\ c_1 = 8$ and $a_2 = 2,\ b_2 = 2$ and $c_2 = 2$

Putting the values in above condition we get:

$\frac{4}{2}\
eq\frac{p}{2}$

$\Rightarrow p\
eq4$

The value of $p$ is not equal to $4$. In other words $p$ can take any value other than $4$.