"Understanding systems of linear equations of two variables" PPT courseware 2

Description

"Understanding systems of linear equations of two variables" PPT courseware 2

learning target

1. Understand the significance of linear equations of two variables and their solutions, systems of linear equations of two variables and their solutions;

2. Be able to identify linear equations of two variables and systems of linear equations of two variables.

main difficulty

Key points: linear equations of two variables and their solutions, linear equations of two variables and the significance of their solutions.

Difficulty: the number of solutions to a linear equation of two variables.

situational navigation

The Great Wall starts from Jiayuguan in the west and ends at Hushan in Liaodong in the east, with a total length of about 7,300 kilometers. The western section is from Jiayuguan to Shanhaiguan, and the eastern section is from Shanhaiguan to Hushan, Liaodong. The western section is about 6,100 kilometers longer than the eastern section. How many kilometers are each of the east and west sections of the Great Wall?

(1) Which quantities are known quantities? What quantities are unknown?

(2) What are the equivalence relationships?

The length of the east section + the length of the west section = 7300 The length of the west section - the length of the east section = 6100

(3) Can you formulate a linear equation of one variable to solve this problem?

Solution: Let the length of the eastern section be x kilometers,

Then the length of the western section is (x+6100) kilometers

The equations are

x+(x+6100)=7300 is 2x+6100=7300

Fierce eyes and golden eyes

The following equations are linear equations of two variables:

(1)x+y+2z=6

(2)xy+4y-5y=9

(3)2x-5=3y+2x

(4)x=y

(5)3x2-2y2=10

(6)2x-3y

(7)3x+5=x-2y

In the problem given by situational navigation, the unknowns x and y must satisfy equations ① and ② at the same time. Put them together and write them as

x + y =7300 ①

y - x =6100 ②

Generally, a set of equations composed of several linear equations is called a system of linear equations!

Like this, a system of linear equations containing two unknowns is called a system of linear equations in two variables.

And x=600 y=6700 is the public solution of equations ① and ②

Like this, the common solution of two equations in a system of linear equations of two variables is called the solution of this system of linear equations of two variables. The process of finding solutions to a system of equations is called solving a system of equations

Think about it: Does the same letter in two equations in a system of equations represent the same quantity?

Class summary

1. Learned the definitions of linear equations of two variables and systems of linear equations of two variables.

2. Learned how to test whether a set of numbers is the solution to a linear equation of two variables or a system of linear equations of two variables.

Consolidate testing

1. Among the following equations, which one is a linear equation of two variables ( )

A.x+2y=3z B. xy=1 C. x+y=1 D. x-y2=2008

2. Regarding the solution to the linear equation of two variables 4x+5y=13, which of the following statements is correct ( )

A. There is only one solution B. There are two solutions

C. There are countless solutions D. Any set of rational numbers is its solution.

3. Which of the following equations is a linear equation of two variables ( ).

3x=2y+5 X-y=1 X=5 X=2y+1

X+y=3x-7 X-m=3 X+y=6 Xy=1

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For more information about the PPT courseware "Understanding Systems of Linear Equations of Two Variables", please click the "Understanding Systems of Linear Equations of Two Variables" ppt tag.

"Understanding systems of linear equations of two variables" PPT courseware 4:

"Understanding Systems of Linear Equations of Two Variables" PPT Courseware 4 If the solution to a linear equation of one variable is listed: Suppose the length of the east section is x kilometers, then the length of the west section is (x+6100) kilometers. The equation of the column is x+(x+6100)=7300 Independent Learning If the length of the eastern section of the Great Wall is x kilometers and the length of the western section is y..

"Understanding systems of linear equations of two variables" PPT courseware 3:

"Understanding Systems of Quadratic Equations" PPT Courseware 3 Scenario Navigation The majestic Great Wall is a symbol of the Chinese nation. The Great Wall starts from the Yalu River in the east and reaches Jiayuguan in the west. It is 7,300 kilometers long. The eastern section is from the Yalu River to Shanhaiguan, and the western section is from Shanhaiguan to Shanhaiguan. Jiayuguan, the western section is longer than the eastern section...

"Understanding systems of linear equations of two variables" PPT courseware:

"Understanding Systems of Quadratic Equations" PPT Courseware Scenario Navigation The majestic Great Wall is the symbol of the Chinese nation. It starts from the Yalu River in the east and reaches Jiayuguan in the west. It has a total length of 7,300 kilometers. The eastern section is from the Yalu River to Shanhaiguan, and the western section is from Shanhaiguan to Jiayuguan. , the western section is 6.. longer than the eastern section.

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Update Time: 2024-11-22

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 2 industry PPT template

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