Question

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

– 3x + 5y = 7 and 2px – 3y = 1,

if the lines represented by these equations are intersecting at a unique point.

Answer 1

Given pair of linear equations is

– 3x + 5y = 7

2px – 3y = 1

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

Here, a₁ = –3, b₁ = 5, c₁ = – 7

And a₂ = 2p, b₂ = – 3, c₂ = – 1

`a_1/a_2 = (-3)/(2p)`

`b_1/b_2 = (-5)/3`

`c_1/c_2` = 7

Since, the lines are intersecting at a unique point i.e., it has a unique solution

`a_1/a_2 ≠ b_1/b_2`

`(-3)/(2p) ≠ (-5)/3`

`p ≠ 9/10`

Hence, the lines represented by these equations are intersect at a unique point for all real values of p except `9/10`.