Question

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

Answer 1

Given:

3x + y - 2 = 0 ——> 1

px + 2y - 3 = 0 ——> 2

2x - y - 3 = 0 ——> 3

Solve for x & y, using equations 1 & 3,

3x + y - 2 = 0
2x - y - 3 = 0
———————
5x - 5 = 0

5x = 5

x = 1 ——> 4

y = -1 ——> 5

Substitute 4 & 5 in equation 2,

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

p -2 -3 = 0

p - 5 = 0

p = 5 ——> Answer