Question

If a pair of linear equations in two variables is consistent, then the lines represented by two equations are

A. intersecting

B. parallel

C. always coincident

D. intersecting or coincident

Answer 1

A pair of linear equations is called inconsistent when the lines doesn’t have any solution. It means both the lines are parallel to each other.

A pair of linear equations is called consistent when they have infinite number of solutions or they have a unique solution.

An intersecting line will always have a unique solution.

A coincident line will have infinite number of solutions.

So the line represented by a pair of linear equations in two variables is always intersecting or coincident if the system of equation is consistent.

Let a₁x + b₁y = c₁ & a₂x + b₂y = c₂ be two lines where

a₁ & a₂ are the coefficients of x

b₁ & b₂ are the coefficients of y

c₁ & c₂ are the constants

For the system of linear equations to have infinitely many solutions we must have

The system of linear equations will have unique solution if

For the system of linear equations to be consistent either condition (i) or (ii) must be satisfied.

If the equations are consistent then they are either intersecting or coincident