Question

Find the value of p for the following pair of equation -3x+5y=7 and 2px-3y=1 if the lines represented by these equations are intersecting at a unique point.

Answer 1

if the lines intersect at a unique point, then a1/a2 ≠ b1/b2 

therefore $-3/2p \neq 5/-3$

ie, 9 ≠ 10 p

ie p ≠ 9/10

hence the required answer 

Answer 2

Answer:-3/2p ≠ 5/-3

2p≠5

P≠5/2

P≠ 2.5

Step-by-step explanation:

Unique point

a1/a2 ≠ b1/b2

a1 = -3 b1= 5

a2= 2p b2=-3

-3/2p ≠ 5/-3

-3 and -3 cancelled

2p ≠5

P≠5/2

P≠2.5

Hence ,p can have any value except 5/2 or 2.5