Question

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

2x + 3y – 5 = 0 and px – 6y – 8 = 0,

if the pair of equations has a unique solution.

Answer 1

Given pair of linear equations is

2x + 3y – 5 = 0

px – 6y – 8 = 0

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

Here, a₁ = 2, b₁ = 3, c₁ = – 5

And a₂ = p, b₂ = – 6, c₂ = – 8

`a_1/a_2 = 2/p`

`b_1/b_2 = - 3/6 = -1/2`

`c_1 /c_2 = 5/8`

Since the pair of linear equations has a unique solution,

`a_1/a_2 ≠ b_1/b_2`

So `2/p ≠ -1/2`

p ≠ – 4

Hence, the pair of linear equations has a unique solution for all values of p except – 4.