Linear Equations System Calculator
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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