Question

Show the table briefing thecondition for linear equations to be intersecting, parallel or co-incident?

Answer 1

Given : Pair of linear equations

To Find : condition for linear equations to be intersecting, parallel or co-incident

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)

a₁/a₂ ≠ b₁/b₂   intersecting lines   hence unique solution

a₁/a₂ = b₁/b₂ = c₁/c₂    co-incident lines  infinite many solutions

a₁/a₂ = b₁/b₂ ≠  c₁/c₂  parallel  lines hence no solution

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