Question

For which value of $p$ does the pair of equation given below has unique solution
$4x+py+8=0$
$2x+2y+2=0$

Answer 1

Given equation:-

$4x+py+8=0$

$a_1=4,b_1=p,c_1=8$

$2x+2y+2=0$

$a_2=2,b_2=2,c_2=2$

Since the given pair of equation hs unique solution.

Therefore,

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

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

$\Rightarrow p\ne 4$

Hence the given pair of equation has unique solution for all values of $p$ except $4$.