1. What is a 2x2 System of Equations?

A 2x2 system of equations consists of two linear equations with two variables (typically x and y). The general form is:

2. How Does the Calculator Work?

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

Where:

• a, b — Coefficients of the first equation
• c — Constant term of the first equation
• d, e — Coefficients of the second equation
• f — Constant term of the second equation
• ae - bd — The determinant of the coefficient matrix

3. Understanding the Solution

Unique Solution: When the determinant (ae - bd) is non-zero, there's exactly one solution.
No Solution: When the equations represent parallel lines.
Infinite Solutions: When the equations represent the same line.

4. Using the Calculator

Tips: Enter all six coefficients (a, b, c, d, e, f) as real numbers. The calculator will show "no unique solution" if the determinant is zero.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "no unique solution"?
A: This means the system is either inconsistent (no solution) or dependent (infinite solutions). Check your equations.

Q2: Can this solve non-linear systems?
A: No, this calculator only works for linear systems of equations.

Q3: What about larger systems?
A: For 3x3 or larger systems, you would need to use other methods like Gaussian elimination.

Q4: Why does the denominator appear in both solutions?
A: The denominator is the determinant of the coefficient matrix, which must be non-zero for a unique solution.

Q5: Can I use fractions or decimals?
A: Yes, the calculator accepts both decimal and fractional inputs (use decimal notation for fractions).