Systems of Linear Equations

The final page focuses on układy równań (systems of equations), particularly first-degree equations with two unknowns.

It introduces the concept of a system of equations and provides examples of different types of solutions: one solution, no solutions, and infinitely many solutions.

Definition: A system of first-degree equations with two unknowns is a set of two or more equations that must be solved simultaneously.

The page covers two main methods for solving systems of equations:

1. Rozwiązywanie układów równań metodą podstawiania (Solving systems of equations by substitution)
2. Rozwiązywanie układów równań metodą przeciwnych współczynników (Solving systems of equations by elimination)

Example: Solving the system {x + 2y = 5, x + 3y = 8} using the substitution method, resulting in y = 1 and x = 3.

Highlight: When using the elimination method, multiply one or both equations by constants to create opposite coefficients for one variable, allowing it to be eliminated when the equations are added or subtracted.

This page provides essential skills for solving układy równań - zadania z rozwiązaniami (systems of equations - problems with solutions) and prepares students for more advanced topics in algebra.