Linear Equations with Two Variables
This section introduces the concept of jedno równanie z dwiema niewiadomymi linearequationswithtwovariables and their graphical representations.
Key points:
- A linear equation with two variables is represented as ax + by = c, where a and b are not both zero
- The graph of a linear equation is a straight line
- Examples are provided, such as 3x + 2y = 4 and 2x - y = 5
Definition: A linear equation with two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and a and b are not both zero.
Example: The equation 2x - y = 5 can be rearranged to y = 2x - 5, which is the slope-intercept form of a line.
The section also introduces układy równań liniowych z dwiema niewiadomymi zadania systemsoflinearequationswithtwovariables and their graphical solutions.
Highlight: The solution to a system of equations is a pair of numbers x,y that satisfies both equations simultaneously.
Solving Systems of Equations
This part covers various methods for rozwiązywanie układów równań pierwszego stopnia z dwiema niewiadomymi solvingfirst−degreesystemsofequationswithtwovariables.
Methods discussed include:
- Rozwiązywanie układów równań metodą podstawiania Substitutionmethod
- Rozwiązywanie układów równań metodą przeciwnych współczynników Eliminationmethod
- Graficzne rozwiązywanie układów równań Graphicalmethod
Example: Using the substitution method to solve the system:
2x - 3y = 1
3x - 4y = 11
The section provides step-by-step solutions for various types of systems, including:
- Systems with one unique solution consistentindependent
- Systems with no solution inconsistent
- Systems with infinitely many solutions consistentdependent
Vocabulary:
- Układ oznaczony: A system with one unique solution
- Układ sprzeczny: A system with no solution
- Układ nieoznaczony: A system with infinitely many solutions