**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-