Question

For what value of p the pair of linear equations (p+2)x-(2p+1)y=3 and (2p-1)2x-3y=7 has unique solutions???? Plss solve it....

Answer 1

Hi ,

I think there is an error in the

question ,

It may be like this .

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

( 2p - 1 )x - 3y - 7 = 0 ----( 2 )

Compare above equations with

a1 x + b1 y + c1 = 0 and

a2 x + b2 y + c2 = 9 , we get

a1 = p + 2 , b1 = -( 2p + 1 ) , c1 = -3 ,

a2 = 2p - 1 , b2 = -3 , c2 = - 7

It is given that ,

Equations has unique solution.

Therefore ,

a1/a2 ≠ b1/b2

( p + 2 )/( 2p - 1 ) ≠ - ( 2p + 1 ) / ( - 3 )

( p + 2 ) 3 ≠ ( 2p + 1 ) ( 2p - 1 )

3p + 6 ≠ ( 2p )² - 1²

3p + 6 ≠ 4p² - 1

4p² - 3p - 7 ≠ 0

4p² - 7p + 4p - 7 ≠ 0

p( 4p - 7 ) + 1 ( 4p - 7 ) ≠ 0

( 4p - 7 ) ( p + 1 ) ≠ 0

4p - 7 ≠ 0 or p + 1 ≠ 0

p ≠ 7/4 or p ≠ -1

I hope this helps you.

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