Linear Equation System Solver
Educational tool for solving 2x2 and 3x3 systems of linear equations. Displays matrix steps and determinant logic.
About
Solving systems of linear equations is a fundamental skill in algebra and physics. This tool handles 2x2 and 3x3 systems using Cramer's Rule, a method that utilizes determinants to find unique solutions. Unlike substitution or elimination, which can become messy with manual calculation, Cramer's Rule provides a structured, algorithmic approach ideal for computer verification.
The solver detects parallel lines (No Solution) and coincident lines (Infinite Solutions) by analyzing the determinant of the coefficient matrix. It outputs the solution vector clearly, allowing students to verify their manual work matrix by matrix.
Formulas
For a 2x2 system, the solution is found via determinants:
Where D is the main determinant:
Reference Data
| System Size | Structure | Determinant (D) | Interpretation |
|---|---|---|---|
| 2x2 | a1x + b1y = c1 a2x + b2y = c2 | a1b2 - a2b1 | Intersection of two lines. |
| 3x3 | x, y, z variables | Computed via Sarrus or Expansion | Intersection of three planes. |