Enter both equations in standard form.
Algebra Calculator
Simultaneous Equations Solver
Solve two linear equations in two unknowns using determinants and check both equations.
Instant answer
Formula breakdown
Browser-based
Mobile friendly
Interactive calculator
Enter your values
Use the example values or replace them with your own. Required validation happens before the calculation.
Ready
Calculated answer
Result
Simple workflow
How to use the Simultaneous Equations Solver
Follow these steps to get a reliable result and understand how it was produced.
Calculate the coefficient determinant.
Use Cramer’s rule and verify x and y in both equations.
Understanding the calculation
Cramer’s rule uses the determinant a₁b₂−a₂b₁. A zero determinant means there is no unique solution.
a₁x+b₁y=c₁ and a₂x+b₂y=c₂The result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Mixture and pricing problems
- Coordinate line intersections
- Two-variable algebra checks
Accuracy tips
- Keep coefficients aligned with x, y, and the result.
- A zero determinant means the lines are parallel or the same line.
- Decimal coefficients are supported.
Helpful answers
Simultaneous Equations Solver FAQs
Important details about formulas, inputs, limitations, and result interpretation.
What does a zero determinant mean?
The equations do not have exactly one solution; they may be inconsistent or represent the same line.
Can I solve more than two variables?
This tool is specifically for a 2×2 system.
What is Cramer’s rule?
It is a determinant-based method for solving a square linear system with a non-zero determinant.
How are answers checked?
The calculated x and y are substituted into both original equations.