System of 2 equations calculator
Solve a 2×2 linear system a₁x + b₁y = c₁, a₂x + b₂y = c₂ by elimination (Cramer’s rule).
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Tool guide
System of 2 equations calculator: how it works
Practical information to understand the result and use this tool correctly.
About System of 2 equations calculator
A 2×2 linear system has a unique solution when the coefficient determinant is non-zero.
Cramer’s rule returns x and y directly; singular cases report parallel or coincident lines.
Common in mixture problems, break-even analysis, and first linear-algebra exercises.
How to use it
- 1Enter six coefficients: a₁,b₁,c₁ and a₂,b₂,c₂.
- 2Calculate x and y (or the singularity message).
- 3Check units match the problem context.
Frequently asked questions
- No solution?
- Parallel distinct lines — inconsistent system.
- Infinite solutions?
- Both equations describe the same line.