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 two linear equations with two variables (x and y) using the elimination method.

2. How Does the Calculator Work?

The calculator uses the following method to solve the system:

The solution is found by calculating the determinant: \[ \text{det} = ae - bd \] If det ≠ 0, the system has a unique solution: \[ x = \frac{ec - bf}{\text{det}}, \quad y = \frac{af - dc}{\text{det}} \]

3. Types of Solutions

Unique Solution: When the determinant is non-zero, the system has exactly one solution.
No Solution: When the lines are parallel and distinct.
Infinitely Many Solutions: When the equations represent the same line.

4. Using the Calculator

Tips: Enter the coefficients (a, b, c, d, e, f) of your system of equations. The calculator will determine if there's a unique solution, no solution, or infinitely many solutions.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "No solution"?
A: This means the equations represent parallel lines that never intersect.

Q2: What does "Infinitely many solutions" mean?
A: This means both equations represent the same line, so every point on the line is a solution.

Q3: Can I solve systems with more than two equations?
A: This calculator only handles systems of two equations with two variables.

Q4: What about non-linear equations?
A: This calculator is designed for linear equations only.

Q5: How precise are the solutions?
A: Solutions are rounded to 4 decimal places for display purposes.