Question

Find "p" x+py=1 , px+y= p² has infinitely many solutions.​

Answer 1

Given : x+py=1 , px+y= p² has infinitely many solutions.​

To Find : Value of p

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others)

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

x+py=1

px+y= p²

infinite solutions

=> 1/p  = p/1  = 1/p²

1/p = p/1  =>  p² = 1  => p  = ±1

1/p  = 1/p²

=> p² = p

=> p(p -1 ) = 0

=> p = 0  , 1

p/1  = 1/p²

=> p³ = 1

=> p = 1

Common from all  is  p  = 1

Hence value of p  is  1

x + y = 1

x + y = 1

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