Question

Find the value of so that the three lines 3x+ y – 2 = 0, px+ 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

Answer 1

The given equation of lines are 

3x + y – 2 = 0              (1) 

2x – y – 3 = 0              (2) 

px + 2y – 3 = 0            (3) 

Solving (1) and (2), we have  

(1) + (2) ⇒ 5x – 5 ⇒ x = 1 

(1) ⇒ 3 + y – 2 = 0 

⇒ y = – 1 

∴ (1, – 1) is the point of intersection of (1) and (2) putting (1, – 1) in equation (3), 

we get, 

p. 1 + 2. (– 1) – 3 = 0 

⇒ p – 5 = 0 

⇒ p = 5