Find the valued of P for which the following pair of linear equation have no solution -x +py= 7 ; px - y = 1
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Answer: 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
no solutions.
= > 1/p = p/1 ≠ 1/p²
1/p = p/1 = > p² = 1 = > p = ±1
p = 1
= > 1/1 = 1/1 =1/1 infinite solution
1/-1 = -1/1 ≠ 1/(-1)² no solution
Hence, value of p is -1 for no solution
x - y = 1
-x + y = 1
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