Page 1: Introduction to Linear Systems and Solution Methods

This page introduces the fundamental concepts of sistemi lineari and their various solution methods. The content begins with the standard form of linear equations and explains different types of systems.

Definition: Linear systems are sets of equations that must be solved simultaneously to find values of x and y that satisfy all equations.

Highlight: Systems can be classified into three types:

• Determined (finite number of solutions)
• Indeterminate (infinite solutions)
• Impossible (no solutions)

The page details three primary solution methods:

1. Metodo di sostituzione (Substitution Method):

   • Solve one equation for one variable
   • Substitute into the other equation
   • Solve resulting equation
   • Back-substitute to find other variable

2. Addition/Subtraction Method:

   • Used when coefficients are equal or opposite
   • Combine equations to eliminate one variable
   • Solve for remaining variable

3. Cramer's Rule:

   • Calculate determinant D
   • Find Dx and Dy
   • Solutions: x = Dx/D, y = Dy/D

Vocabulary: Determinant (D) - A value calculated from the coefficients that helps determine the nature of the solution.