What the system of linear equation in two variabes which has no solution?

Answer 1

For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.)

For example y = mx + b

and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution.

With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.