"System of linear equations in three variables" System of linear equations in two variables PPT courseware

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"System of linear equations in three variables" System of linear equations in two variables PPT courseware

1. Create scenarios and introduce new lessons

It is known that the sum of the three numbers A, B, and C is 23, the number A is 1 greater than the number B, and the sum of twice the number A and the number B is 20 greater than the number C. Find these three numbers.

In the above problem, assuming that the number A is x, the number B is y, and the number C is z, the system of equations can be obtained from the meaning of the question:

x+y+z=23

2x+y-z=20

x-y=1

In the above problem, assuming that the number A is x, the number B is y, and the number C is z, the system of equations can be obtained from the meaning of the question:

2. Learn by analogy and explore new knowledge

Can we solve this system of linear equations in three variables?

What is the difference between elimination when solving a system of linear equations in three variables and elimination when solving a system of linear equations in two variables? When solving the above system of equations, can you first eliminate the unknown y (or z) to obtain the solution to the system of equations?

3. Understand and consolidate

Use the methods you learned to solve equations:

Observe (2), this system of equations is different from the previous ones. The three equations are all missing "who", which one is better to eliminate, and what method should be used to eliminate it?

4.Practical application

There are 651 students in three grades of junior high school in a school. There are 10% more students in eighth grade than in ninth grade. There are 5% more students in seventh grade than in eighth grade. How many students are there in each of the three grades?

5. Class summary

(1) The concept of a system of linear equations in three variables;

(2)Solution to a system of linear equations in three variables;

(3) Let’s talk about the ideas for solving multivariate linear equations.

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

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Update Time: 2024-11-03

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

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