System of Equations Calculator
Solve systems of linear equations with two or three variables step by step using this free calculator that runs in your browser.
Enter Values
How to use this calculator
- Write each equation as ax + by = c and enter the six coefficients.
- Read the values of x and y.
How it works
It solves the pair with Cramer's rule using the determinant a₁b₂ − a₂b₁; if that's zero there's no single solution.
Worked example
2x + 3y = 6 and 4x + 9y = 15. x = 1.5, y = 1.
Common mistakes
- Putting a number on the wrong side — rearrange to ax + by = c first.
- Parallel lines (proportional coefficients) have no single solution.
Frequently asked questions
How do you solve a system of equations?
Find the values that satisfy all equations at once, by substitution, elimination or matrices. Two lines' solution is their intersection point.
What if there's no solution?
Parallel lines never meet (no solution); identical lines overlap (infinitely many solutions). The tool flags both cases.
Why does it sometimes say no unique solution?
If the two lines are parallel (no solution) or identical (infinitely many), there's no single x, y pair — that's when the determinant is zero.
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Cite this tool
Zerdly. (2026). System of Equations Calculator. Retrieved from https://www.zerdly.com/tools/system-of-equations-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.