About this calculator
Enter the coefficients; use negative numbers where needed.
How to use it
- Choose one equation or two.
- Enter the coefficients.
- Read the solution.
The formula
x = (c − b) ÷ a; for two equations, x = (c₁b₂ − c₂b₁) ÷ D, y = (a₁c₂ − a₂c₁) ÷ D, D = a₁b₂ − a₂b₁
- D
- determinant; if 0, the lines are parallel or the same
Worked example
Two equations
- 2x + 3y = 13 and x − y = −1.
- D = 2 × (−1) − 1 × 3 = −5.
- x = 2, y = 3.
What the result means
Check by putting the answer back into both equations.
Assumptions
- All lengths in the same unit.
Limitations
- Results are rounded to 10 significant figures.
Frequently asked questions
How do I solve two linear equations?
By substitution, elimination or Cramer’s rule; all give the same answer.
What if D = 0?
The lines are parallel (no solution) or the same line (infinitely many).
What is 3x + 7 = 22?
x = 5.
Last reviewed on 3 October 2026. Found a mistake? Tell us.