1. What is a 3 Variable System Of Equations?

A system of three linear equations with three variables (x, y, z) is a set of equations that can be represented as shown above. The solution is the set of values (x, y, z) that satisfies all three equations simultaneously.

2. How Does the Calculator Work?

The calculator uses Cramer's Rule to solve the system:

Where D is the determinant of the coefficient matrix, and Dₓ, Dᵧ, D_z are determinants with one column replaced by the constants.

3. Solving Methods

Methods: The calculator uses matrix determinants (Cramer's Rule). Other methods include substitution, elimination, and matrix inversion.

4. Using the Calculator

Tips: Enter coefficients for all three equations. The system must be linear and independent for a unique solution.

5. Frequently Asked Questions (FAQ)

Q1: What if the determinant is zero?
A: A zero determinant means no unique solution exists (either no solution or infinitely many solutions).

Q2: Can this solve non-linear systems?
A: No, this calculator only solves linear systems. Non-linear systems require different methods.

Q3: What's the maximum number of solutions?
A: A linear system can have: 1 unique solution, no solution, or infinitely many solutions.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places. Very small determinants may lead to precision issues.

Q5: Can I solve 2 or 4 variable systems?
A: This calculator is specifically designed for 3 variable systems only.