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