"Linear equations and linear functions of two variables" PPT courseware for linear equations of two variables 2

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"Linear equations and linear functions of two variables" PPT courseware for linear equations of two variables 2

Review and Thoughts

What is the connection between a system of linear equations in two variables and a linear function?

The solution of a system of linear equations of two variables is the intersection coordinate of their corresponding graphs of two linear functions; conversely, the intersection point of the graphs of two linear functions is also the solution of their corresponding system of linear equations of two variables.

Because of this, equation problems can be solved by knowledge of functions, and conversely, function problems can also be solved by knowledge of equations.

Discuss:

Places A and B are 100 kilometers apart. Two people, A and B, ride bicycles toward each other from places A and B respectively. Assuming that they all keep driving at a constant speed, the distance s (kilometers) between each of them to point A is a linear function of the riding time t (hour). After 1 hour, B is 80 kilometers away from point A; after 2 hours, A is 80 kilometers away from point A. 30 kilometers above ground.

Question: How long did it take for the two to meet?

A certain long-distance bus terminal stipulates that passengers can carry luggage of a certain mass for free, but if it exceeds this mass, they need to purchase a luggage ticket, and the luggage fee y (yuan) is a linear function of the luggage mass x (kilograms). Now we know that Li Ming brought 60 kilograms of luggage and paid a luggage fee of 5 yuan; Zhang Hua brought 90 kilograms of luggage and paid a luggage fee of 10 yuan.

(1) Write the function expression between y and x;

(2) How many kilograms of luggage can passengers carry for free?

In order to encourage residents to save water, a city's water company adopts a segmented charging method based on monthly water consumption. If a household's water fee y (yuan) is payable, the functional relationship between the water consumption x (tons) is as shown in the figure.

(1) Write the functional relationship between y and x when 0≤x≤15 and x>15 respectively;

(2) If a user consumes 10 tons of water in October, how much water fee should he pay? If the user paid a water bill of 51 yuan in November, how many tons of water did he use in that month?

What did you gain from this class?

General steps for finding linear function expressions using systems of linear equations of two variables:

1. Use the coefficients containing letters to set up the expression of a linear function: y=kx+b(k≠0);

2. Substitute the known conditions into the above expression to obtain a system of linear equations of two variables k and b;

3. Solve this system of linear equations of two variables to obtain k, b, and then obtain the expression of the linear function.

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For more information about the PPT courseware "System of linear equations in two variables, linear equations in two variables and linear functions", please click the "System of linear equations in two variables ppt linear equations in two variables and linear functions ppt" tag.

"Linear equations and linear functions of two variables" System of linear equations of two variables PPT courseware 3:

"Linear Equations and Functions of Two Variables" PPT Courseware for Linear Equations of Two Variables 3 Knowledge comes from understanding that two straight lines are parallel to each other and have ________ intersection points; two straight lines coincide and have ________ intersection points; two straight lines intersect and have ________ intersection points; ________ intersection; the equation x+y=5 can...

"Linear equations and linear functions of two variables" PPT courseware for systems of linear equations of two variables:

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Update Time: 2024-09-09

This template belongs to Mathematics courseware Beijing Normal University eighth grade first volume mathematics industry PPT template

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