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

Solution:

The equation of the given line are

3x + y - 2 = 0 ....(1)

px + 2 y - 3 = 0 ....(2)

2x - y - 3 = 0 ....(3)

On solving equations (1) and (3), we obtain

x = 1 and y = - 1

Since these three lines may intersect at one point, the point of intersection of lines (1) and (3) will also satisfy line (2)

p (1) + 2(- 1) - 3 = 0

p - 2 - 3 = 0

p = 5

Thus, the required value of p = 5

NCERT Solutions Class 11 Maths Chapter 10 Exercise ME 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

Summary:

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 is 5