GATE 2018 SYLLABI
Unique, Infinite, Many, Consistent, Inconsistent Solutions ?

1) a₁x + b₁y = c₁
2) a₂x + b₂y = c₂

If
a₁/a₂ ≠ b₁/b₂ 
Than, its called unique solution.it means intercepting lines.Its also called consistent solution.

If
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Than its called no solution. It means parallel lines. Its also called inconsistent solution.

If
a₁/a₂ = b₁/b₂ = c₁/c₂
Than, its called infinite many soluiton. It means coincident lines.Its also called consistent solution.

For example-