1. What is a System of Equations?

A system of linear equations consists of two or more equations with the same set of variables. This calculator solves systems of the form:

2. How Does the Calculator Work?

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

Where:

• \( a, b \) — Coefficients of the first equation
• \( d, e \) — Coefficients of the second equation
• \( c, f \) — Constants on the right side
• \( ae - bd \) — The determinant of the coefficient matrix

Explanation: The solution is found by calculating the ratios of determinants when the system has a unique solution.

3. Understanding the Solution

Details: The solution represents the point of intersection of the two lines represented by the equations. If the determinant is zero, the lines are either parallel or coincident.

4. Using the Calculator

Tips: Enter all six coefficients (a, b, c for the first equation and d, e, f for the second equation). The calculator will display the solution or indicate if no unique solution exists.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "no unique solution"?
A: This means the determinant (ae-bd) is zero, indicating either no solution (parallel lines) or infinitely many solutions (same line).

Q2: Can this solve non-linear systems?
A: No, this calculator only solves linear systems of two equations with two variables.

Q3: What about systems with more equations?
A: This calculator is designed for 2×2 systems. Larger systems require different methods.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places for readability.

Q5: Can I use fractions or decimals?
A: Yes, the calculator accepts both decimal and integer inputs.