Question

Question 9 Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

Class X1 - Maths -Straight Lines Page 233

Answer 1

concept : if lines meet at the same point , then they are concurrent.

Here, equation of lines are
3x + y - 2 = 0 ---------------(1)
Px + 2y -3 = 0--------------(2)
2x - y - 3 = 0 ----------------(3)

adding equations (1) and (3) , we get
(3x + y - 2) + ( 2x - y - 3) = 0
5x - 5 = 0
x = 1 , put it in equation (1)
3 × 1 + y -2 = 0
3 + y - 2 = 0
y = -1
so, the point (1 , -1) Let A
point A will satisfy equation (2) . [ because all of these line intersect at one point e.g (1, -1) .]
P × 1 + 2 × (-1) - 3 = 0
P - 2 - 3 = 0
P - 5 = 0
P = 5

Answer 2

Step-by-step explanation:

just use the concept that if lines are concurrent, determinant =0