A pair of linear equations which has no solution, is called ___________.

A pair of linear equations which has no solution, is called an inconsistent 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:

$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\ne \frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$ {criteria for inconsistency}.

A pair of linear equations having no solutions will represent parallel lines when plotted on a graph.