Question

write the relation between the coefficient of constant and inconstant pair of linear equation​

Answer 1

Answer:

When a linear pair of equations has one solution (intersecting lines) or infinitely many solutions (coincident lines), we say that it is a consistent pair. On the other hand, when a linear pair has no solution (parallel, non-coincident lines), we say that it is an inconsistent pair

Answer 2

Given :   pair of linear equation​

To find :  relation between the coefficient for Consistent & inconsistent pair of linear equation​

Solution:

Let say pair of linear equation is

a₁x  + b₁y  + c₁ = 0

a₂x + b₂y  + c₂ = 0

When pair of linear equation has solution then its called consistent

of there is no solution then its inconsitent

Relation between the coefficient of Consistent & inconsistent pair of linear equation​

a₁/a₂  =  b₁/ b₂  = c₁/c₂    (infinite solutions , Same line , consistent)

a₁/a₂  =  b₁/ b₂  ≠ c₁/c₂    (No solutions , parallel lines , Inconsistent)

a₁/a₂  ≠  b₁/ b₂  ( unique solution , Consistent)

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