System of Equations Calculator 2025: Complete Guide
Struggling with systems of equations? Our 2025 solver handles 2×2 and 3×3 instantly using elimination, substitution, or matrices — with full step-by-step proof.
The 3 Core Methods
Elimination: Add/subtract to cancel a variable
Substitution: Solve one equation and plug in
Matrices: Use determinants or row reduction
Step-by-Step: 2x + 3y = 10, x + 4y = 11
- Multiply 2nd eq by 2: 2x + 8y = 22
- Subtract: (2x + 3y) - (2x + 8y) = -12 → -5y = -12
- y = 2.4
- x = 11 - 4(2.4) = 1.4
- x = 1.4, y = 2.4
Real-World Uses
- Supply & demand economics
- Mixture problems
- Engineering circuits
FAQs
No solution? Parallel lines → inconsistent
Infinite solutions? Same line → dependent
Conclusion
Never fail a system again. Enter your equations now!
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