🎓 Mathematics • Algebra
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Equation Solver
Algebraic solver for single-variable equations and systems of two equations with two unknowns.
Algebra & Matrix Engine
Algebra & Matrix Studio
Solve quadratic equations with complex roots, 2x2 systems via Cramer's rule, binomial FOIL expansions, and 2x2/3x3 matrix linear algebra with instant proofs.
Solver Mode
Standard linear equation form: ax + b = c
Single Variable Linear Equation
3x + 7 = 22
x = 5
Step-by-Step Algebraic Isolation
Original equation: 3x + 7 = 22
Subtract 7 from both sides: 3x = 22 - (7) = 15
Divide both sides by 3: x = 15 / 3
Final solution: x = 5
What is an Equation Solver?
An equation solver finds variable values that satisfy mathematical equalities.
Systems of linear equations find intersection coordinates (x, y) where multiple lines cross.
Formula & Step-by-Step Calculation
x = (c₁b₂ - c₂b₁) / (a₁b₂ - a₂b₁)
Cramer’s determinant rule for simultaneous linear systems.
Worked Step-by-Step Examples
Example 1
Solve 2x + 4 = 10
Solution: x = 3
• 2x = 6 ⟹ x = 3
Common Real-World & Academic Use Cases
- ✓ Break-even economics
- ✓ Electrical circuit loop currents
- ✓ Algebraic problem sets
How to Use the Equation Solver
1
Choose System
Select 1 or 2 variables.
2
Input Coefficients
Enter numbers.
3
View Roots
Inspect exact values.
Frequently Asked Questions
Q: What is Cramer’s Rule?
An explicit algebraic formula for solving systems of linear equations using determinants.