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"Linear functions and systems of linear equations of two variables" PPT courseware for linear functions 2
Induction: the relationship between linear equations of two variables and linear functions
1. Each linear equation of two variables corresponds to a linear function, and therefore also corresponds to a straight line;
2. The coordinates of each point on the straight line are the solutions to the corresponding linear equations of two variables.
1. Draw the straight line corresponding to the linear equation of two variables 3x+5y=8 and 2x-y=1 in the same coordinate system.
⑴Observation: Do these two straight lines intersect?
⑵Thinking: Is this intersection coordinate the solution to the equation system 3x+5y=8 2x-y=1? Why?
General steps for solving a system of linear equations in two variables using the graphical method:
⑴Convert the two equations into the form of a linear function y=kx+b;
⑵ Then draw their images in the same rectangular coordinate system;
⑶ Determine the coordinates of the intersection of the two straight lines.
Example: A telecommunications company provides customers with two ways to charge for Internet access: Method A charges 0.1 yuan per minute based on Internet time; Method B charges a monthly base fee of 20 yuan and charges 0.05 yuan per minute based on Internet time. Regarding billing, how to choose a charging method to make it more cost-effective for Internet users?
summary:
⑴The relationship between linear equations (groups) of two variables and linear functions;
⑵ Look at the system of linear equations of two variables from the two aspects of “number” and “shape”;
⑶Method: Understand and solve problems from the perspective of functions, and solve linear equations of two variables using the image method
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