Page 1: Steps for Graphical Method

The first page outlines the initial steps for solving systems of equations graphically.

Highlight: The graphical method involves transforming equations and plotting lines to find their intersection.

Step 1: Transform each equation to y = ax + b form

• Example: 2x + 2y = -6 becomes y = -x - 3
• Example: 10x - 5y = 30 becomes y = 2x - 6

Step 2: Calculate characteristic points for each line

• Find x and y intercepts or other easily calculated points

Step 3: Plot both lines on a coordinate system

• Use the calculated points to accurately draw each line

Example: For y = -x - 3, points (-1, -2) and (0, -3) are plotted Example: For y = 2x - 6, points (0, -6) and (3, 0) are plotted

The page includes a graph showing both lines plotted, with the point of intersection visible.

Vocabulary: Układy równań metodą graficzną zadania PDF - Systems of equations using graphical method problems PDF

Page 3: Completing the Example

The final page completes the graphical solution for the new example.

Full graph of the system:

• Both lines y = -x + 1 and y = -x - 3 are clearly plotted
• The point of intersection is marked as P(-1, -2)

Highlight: The solution to this system is x = -1 and y = -2.

Example: Rozwiąż graficznie układ równań funkcja kwadratowa - Solve graphically a system of equations with a quadratic function

The page reinforces the importance of accurate graphing and careful reading of the intersection point.

Quote: "Rozwiązanie: x = -1, y = -2" (Solution: x = -1, y = -2)

This example demonstrates how the Metodą graficzną układ równań can be applied to different types of linear systems, providing a visual representation of the solution.