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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.

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Solution

Given pair of linear equations is
- x + py – 1 = 0
and px – y – 1 = 0
On comparing with ax +by + c = 0, we get
a1=1, b1=p and c1=1a2=p, b2=1 and c2=1
Since, the pair of linear equations has no solution i.e., both lines are parallel to each each other.
a1a2=b1b2c1c21p=p111
p2 = 1
p = 1,1
But, we also know
b1b2c1c2
p 1
The value of p is 1.

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