Question

What should be the positive value of $p$ if the pair of equations has no solution?

$x+py=1andpx+y=8,$

Answer 1

Given equations,

$x+py=1,px+y=8$

For the equations to have no solution, the lines must be parallel, so,

i.e. $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

$\frac{a_1}{a_2}=\frac{1}{p},\frac{b_1}{b_2}=\frac{p}{1},\frac{c_1}{c_2}=\frac{1}{8}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}⟹p=\pm 1$

The positive value of $p$ required is $1$