Linear Equations System Calculator

Equation 1: a₁x + b₁y = c₁

x + y = 1

Equation 2: a₂x + b₂y = c₂

x - y = 1

Demo Examples

Introduction to Linear Equation Systems

A system of two linear equations contains two unknowns in standard form: a₁x + b₁y = c₁ and a₂x + b₂y = c₂

Cramer's Rule

D = a₁b₂ - a₂b₁
x = Dₓ/D = (c₁b₂ - c₂b₁)/D
y = Dᵧ/D = (a₁c₂ - a₂c₁)/D

Determinant Information

The system determinant D = a₁b₂ - a₂b₁ determines the nature of solutions:

  • D ≠ 0: Unique solution
  • D = 0 and consistent system: Infinite solutions
  • D = 0 and inconsistent system: No solution