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Authoritative PPT Summary
"Understanding systems of linear equations of two variables" PPT courseware
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?
Question 1: Can you use linear equations to solve problems?
Question 2: If the length of the eastern section of the Great Wall is x kilometers and the length of the western section is y kilometers, can you make equations? Give it a try.
learning target
1. Be able to identify linear equations of two variables and systems of linear equations of two variables;
2. Understand the solutions of linear equations of two variables and systems of linear equations of two variables.
main difficulty
Focus: The meaning of linear equation of two variables.
Difficulty: the meaning of solutions to a system of linear equations in two variables.
Knowledge point 1: The concept of linear equation of two variables
x + y =7300 ①
y - x =6100 ②
These two equations have integers on both sides, contain ______ unknowns, and the terms of the unknowns are all of ______ degree. Such equations are called linear equations of two variables.
Knowledge point 2: Solution of 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)
Like this, the value of a pair of unknowns that fits a linear equation of two variables is called a solution to the linear equation of two variables.
Induction: There are countless solutions to a linear equation of two variables.
Knowledge point 3: System of linear equations in two variables
Like this, when two linear equations of two variables are combined and there are two unknowns, a system of linear equations of two variables is formed.
The same letter in two equations of a system of equations represents the same quantity.
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. The equation 2x2m+3+3y5n-7=4 is a linear equation of two variables with respect to x and y, then m=____, n=___.
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.
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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 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 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,...