Question

For what value of p the pair of linear equations (p+ 2)x - (2p + 1)y = 3(2p -1) and 2x- 3y = 7 has a unique solution.

Answer 1

The Given pair of  linear equation is :
(p+ 2)x - (2p + 1)y  =  3(2p -1) ……….(1)
2x-  3y  = 7 ………….(2)

On comparing with General form of a pair of linear equations  in two variables x & y is:
a1x + b1y + c1 = 0
and   a2x + b2y + c2= 0

a1= (p+2) , b1= - (2p+1), c= - (3(2p -1))
a2= 2 , b2= -3 , c= -7

a1/a2= (p+2) /2 ,  b1/b2=  -(2p+1)/-3

Given: A pair of linear equations has a Unique solution, if
a1/a2 ≠ b1/b2
(p+2) /2 ≠ -(2p+1)/-3
-3(p+2) ≠ 2(-2p-1)
-3p -6 ≠ -4p -2
-3p + 4p ≠ - 2 +6
p ≠ 4
Hence, the value of p ≠ 4

HOPE THIS WILL HELP YOU...