Question

If px+3y-(p-3)=0,12x+py-p=0 has infinite solutions then find p.

Answer 1

Infinite Solutions mean that the two lines are Co-incident

Hence:-

Conditions for infinite solutions is :-

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

$\rule{200}{2}$

Two equations are :-

px + 3y -(p-3) = 0

12x+py - p=0

$\rule{200}{2}$

Applying the condition:-

$\dfrac{p}{12}=\dfrac{3}{p}=\dfrac{-(p-3)}{-p}\\ \\ \\ \dfrac{p}{12}=\dfrac{3}{p}=\dfrac{p-3}{p}\\ \\ \\TAKING\:FIRST\:TWO\:EQUATIONS:-\\ \\ \\ \dfrac{p}{12}=\dfrac{3}{p}\\ \\ \\p^2=12*3\\ \\ \\p^2=36\\ \\ \\p= \sqrt{36} = 6$

$\rule{200}{2}$

Thus,

p=6