Question

Question 4 (ii)
Find the value(s) of p for the following pair of equations – x + py = 1 and px – y = 1, if the pair of equations has no solution.

Answer 1

Given pair of linear equations is
- x + py – 1 = 0
and px – y – 1 = 0
On comparing with ax +by + c = 0, we get
$a_1=-1,b_1=pand{c}_1=-1a_2=p,b_2=-1and{c}_2=-1$
Since, the pair of linear equations has no solution i.e., both lines are parallel to each each other.
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}\Rightarrow \frac{-1}{p}=\frac{p}{-1}\ne \frac{-1}{-1}$
$\Rightarrow$ $p^2$ = $1$
$\Rightarrow$ $p$ = $1,-1$
But, we also know
$\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
$\Rightarrow$ $p$ $\ne$ $-1$
$\therefore$ The value of $p$ is 1.