Cramer's Rule Calculator: The Ultimate Linear System Solver
Welcome to the most powerful Cramer's Rule Calculator available online. This free tool solves 2×2 and 3×3 systems of linear equations using the determinant method, showing every step from matrix formation to final solution. Whether you're a student, teacher, or professional, our Cramer's Rule Calculator delivers accurate results with complete mathematical transparency.
How to Use the Cramer's Rule Calculator
Using our Cramer's Rule Calculator is simple and intuitive:
- Select System Size: Choose between 2×2 or 3×3
- Enter Coefficients: Fill in the left-side values
- Input Constants: Enter the right-side values after equals
- Click Calculate: Get instant step-by-step solution
Solve 2×2 Systems with Cramer's Rule Calculator
For the system:
2x + 3y = 8
4x - y = 7
The Cramer's Rule Calculator computes:
D = |2 3| = 2(-1) - 3(4) = -14
|4 -1|
Dx = |8 3| = 8(-1) - 3(7) = -29
|7 -1|
x = Dx/D = -29/-14 ≈ 2.0714
Solve 3×3 Systems with Cramer's Rule Calculator
The Cramer's Rule Calculator handles complex 3×3 systems effortlessly:
x + 2y + 3z = 14
2x - y + z = 1
3x + y - 2z = 0
It calculates D, Dx, Dy, Dz and divides each by D to find x, y, z.
Step-by-Step Solution Process
Our Cramer's Rule Calculator shows:
- Main coefficient matrix determinant (D)
- Modified matrices with replaced columns
- Individual determinants (Dx, Dy, Dz)
- Final variable values with full calculations
- Visual matrix representations
Advantages of Using Cramer's Rule Calculator
- Visual Learning: See every determinant matrix
- Step-by-Step: Complete algebraic reasoning
- Error Detection: Warns about zero determinant
- Global Use: Works with any real coefficients
- Educational: Perfect for learning and teaching
Applications of Cramer's Rule
- Engineering: Circuit analysis, structural loads
- Economics: Market equilibrium models
- Physics: Force and motion calculations
- Computer Graphics: 3D coordinate transformations
- Operations Research: Resource allocation problems