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"Understanding systems of linear equations of two variables" PPT courseware 3
situational navigation
The majestic Great Wall is a symbol of the Chinese nation. It starts from the Yalu River in the east and reaches Jiayuguan in the west, with 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 6,100 kilometers longer than the eastern section. How many kilometers are the east and west sections of the Great Wall each?
Mark known quantities, unknown quantities, and equivalent relationships
Self-learning
If the eastern section of the Great Wall is x kilometers long and the western section is y kilometers long, then the total length of the Great Wall is ___________ kilometers, and the western section is __________ kilometers longer than the eastern section.
According to the equivalence relationship: the length of the eastern section + the length of the western section = 7300 kilometers, the equation can be written___________
According to the equivalence relationship: the length of the western section - the length of the eastern section = 6100 kilometers, the equation can be written___________
Knowledge point 1: linear equation of two variables
x + y =7300 y - x =6100
These two equations,
1.Both sides are integers
2. There are ______ unknowns.
3. And the degree of the unknown terms contained is ______ times.
Like this, an equation where both sides are integers, contains two unknowns, and the terms containing the unknowns are all linear equations is called a linear equation of two variables.
Knowledge point 2: Solutions to linear equations of two variables Thoughts
1. What is the solution of an equation? How many solutions does a linear equation of one variable have? How to check whether x=3 is the solution of equation 2x-5=0?
2. What is the solution of a linear equation of two variables? How does it differ from the solution to a linear equation of one variable?
3. How many solutions does a linear equation of two variables have? Is any pair of numbers the solution to a linear equation of two variables? How to check whether a pair of numbers is the solution of 2x + y =3?
4. How to write the solution of a linear equation of two variables?
Determine whether the values of x and y given in the following brackets are solutions to the previous equation
(1) 2x-3y=6 (x=0, y=4)
(2) 5x+2y=8 (x=2, y=-1)
(3) 2y=4+x (x=2, y=2)
Definition: Like this, the values of a pair of unknowns that fit a linear equation of two variables are called solutions to the linear equation of two variables.
Induction: There are countless solutions to a linear equation of two variables.
Cooperation and exchange
x + y =7300
y - x =6100
This forms a system of linear equations of two variables
think:
1. Does every equation in the system of linear equations of two variables have to be a linear equation of two variables? (Textbook P50 Challenge yourself)
2. What are the writing requirements for systems of linear equations of two variables?
pay attention
The same unknowns in both equations represent the same quantities! (Combined with situational navigation)
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.
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"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 2:
"Understanding linear equations of two variables" PPT courseware 2 Learning objectives 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. Key points and difficulties Key points: linear equations of two variables and their solutions,...
"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.