Systems of Equations Solver (3×3)
How It Works
This systems of equations solver (3×3) uses established formulas to provide accurate results.
The basic rule:
- a₁x + b₁y + c₁z = d₁
- a₂x + b₂y + c₂z = d₂
- a₃x + b₃y + c₃z = d₃
- Cramer's Rule: x = Dx/D, y = Dy/D, z = Dz/D
Results are estimates. Consult a professional for critical decisions.
Want to Actually Learn Algebra?
Calculators give you answers — but if you want to understand the math, Allday Everyday Math teaches Algebra 1 fast with structured lessons, worked examples, and practice quizzes that build real confidence.
Explore Allday Everyday Math →Frequently Asked Questions
How do you solve a 3×3 system of equations?
Common methods include Gaussian elimination (row reduction), Cramer's Rule (using determinants), and substitution. This calculator uses Cramer's Rule to find exact solutions.
What does the determinant tell you?
If the determinant is zero, the system has either no solution or infinitely many solutions. A nonzero determinant guarantees exactly one unique solution.
When do you use 3×3 systems in real life?
Three-variable systems appear in physics (force equilibrium), chemistry (balancing reactions), economics (supply-demand models), and circuit analysis (Kirchhoff's laws).