System of Equations Calculator
Enter the coefficients of the two equations.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Determinant D = a₁b₂ − a₂b₁
- x = (c₁b₂ − c₂b₁) ÷ D
- y = (a₁c₂ − a₂c₁) ÷ D
For a single quadratic equation, use the quadratic equation calculator.
Worked example
2x + 3y = 13 and x − y = −1:
- D = −2 − 3 = −5
- x = 2 and y = 3
Why your number may differ
Results are rounded to 6 decimal places. Systems with three or more unknowns need a larger solver.
Frequently asked questions
How do I solve two equations?
You can use substitution, elimination or Cramer’s rule. This calculator uses Cramer’s rule with determinants.
What does it mean when there is no unique solution?
The determinant is 0, so the two lines are either parallel (no solution) or the same line (infinite solutions).
How can I check the answer?
Put x and y back into both equations. Both must be true.