Pair of Linear Equations in Two Variables | Pair of Linear Equations in Two Variables - Exercise 3.3

Question

– 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point. Find p.

Accepted Answer

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;

a₁ /a₂ = -3/ 2p

b₁ /b₂ = – 5/3

c₁ /c₂ = 7

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

a₁/a₂ ≠ b₁/b₂

-3/2p ≠ -5/3

p ≠ 9/10

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

Question 31