A pair of linear equations in two variables, which has a solution or multiple solutions, is ____________.

A pair of linear equations in two variables, which has a unique solution or infinitely many solutions, is called a consistent pair of linear equations.

This can also be understood if the pair of linear equations follow the criterion given below:

If the two linear equations are of the form:

${\mathrm{a}}_1\mathrm{x}+{\mathrm{b}}_1\mathrm{x}+{\mathrm{c}}_1=0$

${\mathrm{a}}_2\mathrm{x}+{\mathrm{b}}_2\mathrm{x}+{\mathrm{c}}_2=0$

Then,

 For Unique solution, (Shows intersecting lines when plotted on a graph)

$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}\ne \frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\ne \frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$  {Consistent}

And, for infinitely many solutions (Shows coincident lines when plotted on a graph).

$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$ {Consistent}