Question

A pair of linear equations 111 2 2 2 ax by c ax by c + += + += 0, 0 is said to be
inconsistent if

Answer 1

Given : Pair of linear Equations  a₁x + b₁y  + c₁ = 0   &  a₂x  + b₂y + c₂  = 0

To find : When is the pair of linear equations  is inconsistent

Solution:

a₁x + b₁y  + c₁ = 0  

 a₂x  + b₂y + c₂  = 0

inconsistent When there is no solution

iff  a₁ /a₂  =  b₁/b₂ ≠ c₁/ c₂

Additional info

consistent

if   a₁ /a₂  =  b₁/b₂ = c₁/ c₂   ( Infinite Solutions)

consistent

a₁ /a₂  ≠   b₁/b₂    ( unique Solution)

pair of linear equations is said to be  inconsistent if

a₁ /a₂  =  b₁/b₂ ≠ c₁/ c₂

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