Two-Variable System of Linear Equations Solver
Local ProcessingSolve simultaneous linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ using Cramer's rule.
How It Works & Processing Standards
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Enter the six coefficients of both equations and x and y are found with Cramer’s rule.
How to Use Two-Variable System of Linear Equations Solver
- 1First equationa₁, b₁ and c₁ of a₁x + b₁y = c₁.
- 2Second equationa₂, b₂ and c₂. Negatives are fine.
- 3Read the solutionx and y if there is one solution; otherwise "no solution" or "infinitely many".
Examples
2x + 3y = 13, x − y = −1
Input: 2, 3, 13 / 1, −1, −1
Result: x = 2, y = 3
x + y = 10, 2x + 4y = 28
Input: 1, 1, 10 / 2, 4, 28
Result: x = 6, y = 4
Common Use Cases
- Checking simultaneous equation homework
- Prices or quantities that satisfy two conditions
- Mixture ratio problems
Frequently Asked Questions (FAQ)
What does "no solution" mean?
The two lines are parallel and never meet. Infinitely many solutions means both equations describe the same line.
What about three unknowns?
This tool handles two.