Question

Find the value of p for which the given pair of equations 2x+3y-5=0,px-6y-8=0 has a unique solution .

Answer 1

Solution :

Compare

2x + 3y - 5 = 0 ----( 1 )

px - 6y - 8 = 0 ----( 2 )

wiith a1x + b1y + c1 = 0 and

a2x + b2y + c2 = 0 , we get

a1 = 2 , b1 = 3 , c1 = -5 ;

a2 = p , b2 = -6 , c2 = -8 ;

Now ,

a1/a2 ≠ b1/b2 [ Given unique solution ]

2/p ≠ 3/(-6)

=> 2/p ≠ 1/-2

=> -4 ≠ p

Therefore ,

p € R , p ≠ 4

••••

Answer 2

Answer:

2x+3y-5=0

px-6y-8=0

A1/A2=B1/B2 =C1/C2

2/P≠1/-2≠-5/-8

THEREFORE P≠4