Question

if 3x+2y-4=0 and px-y-3=0 represent intersecting lines find p

Answer 1

Condition of intersecting lines
a1 / a2 =/=b1 / b2 =/= c1 / c2

GIVEN
3x + 2y -4 =0
px - y - 3 = 0
Equate both equation, we will Equate y
3x + 2y - 4 =0
2px - 2y - 6 = 0
Sum
(3 + 2p)x - 10 = 0
(3 + 2p)x = 10
x = 10 / (3 + 2p)
Subsitute in (1)
3 ( 10 / (3 + 2p) + 2y - 4 =0
(30 /3 + 2p) + 2y = 4
y = 4 - [30 / (3 + 2p)] / 2
y = (12 + 8p - 30) / 6 + 4p
y = - 18 + 8p / 6 + 4p
y = - 9 + 4p / 3 + 2p
Subsitute x and y in (2)
p[10 / (3 + 2p)] - (- 9 + 4p / 3 + 2p) = 3
10p + 9 - 4p = 9 + 6p
6p - 6p = 9 - 9
0 = 0
Therefore, value of p is zero.