Question

Find the value(s) of p in (i) to (iv) and p and q in (v) 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  ......(i)

px – y – 1 = 0  ......(ii)

On comparing with ax + by + c = 0, we get

a₁ = –1, b₁ = p, c₁ = –1

a₂ = p, b₂ = – 1, c₂ = –1

`a_1/a_2 = (-1)/p`

`b_1/b_2` = – p

`c_1/c_2` = 1

Since, the lines equations has no solution i.e., both lines are parallel to each other.

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

`(-1)/p` = – p ≠ 1

Taking last two parts, we get

p ≠ –1

Taking first two parts, we get

p² = 1

p = ±1

Hence, the given pair of linear equations has no solution for p = 1.