Linear Equations Solver

What is a System of Linear Equations?

A system of linear equations consists of two or more linear equations with the same variables. For example:

Solution Methods

• Substitution Method
  • Solve one equation for a variable
  • Substitute into other equations
  • Best for simple systems
• Elimination Method
  • Add or subtract equations
  • Eliminate variables one by one
  • Effective for larger systems
• Gaussian Elimination
  • Convert to row echelon form
  • Back substitution
  • Systematic approach

Types of Solutions

Matrix Representation

Systems can be written as Ax = b where:

• A is the coefficient matrix
• x is the variable vector
• b is the constant vector

Applications