Find the value of so that the three lines 3x+ y – 2 = 0, px+ 2y –

1.	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» 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

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»

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