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Category | Format | Size |
---|---|---|
Hebei Education Edition Seventh Grade Mathematics Volume 2 | pptx | 6 MB |
Description
"Simple Three-dimensional Linear Equations" PPT courseware
Part One: Review and New Knowledge
Knowledge review
What are the methods to solve a system of linear equations in two variables? What is their essence?
New course introduction
question
Xiao Ming has 12 banknotes with denominations of 1 yuan, 2 yuan, and 5 yuan on hand, totaling 22 yuan. The number of 1 yuan banknotes is 4 times the number of 2 yuan banknotes. Find the number of 1 yuan, 2 yuan, and 5 yuan banknotes. How many.
analyze:
This problem contains _____ equality relations:
The number of 1-yuan banknotes + the number of 2-yuan banknotes + the number of 5-yuan banknotes = 12
The number of 1-yuan banknotes = 4 times the number of 2-yuan banknotes
The amount of 1 yuan + the amount of 2 yuan + the amount of 5 yuan = 22 yuan
Let 1 yuan, 2 yuan, and 5 yuan banknotes be x, y, and z respectively.
According to the meaning of the question, the following three equations can be obtained:
X+y+z=12
X=4y
X+2y+5z=22
What can you conclude by observing equations ① and ③?
Both contain three unknowns, and the degree of the terms containing the unknowns are all 1. An equation like this is called a linear equation of three variables.
Simple three-dimensional linear equation system PPT, part 2 content: knowledge points
The system of equations contains three identical unknowns, the degree of the terms containing the unknowns in each equation is 1, and there are three equations in total. Such a system of equations is called a system of linear equations of three variables.
Example 1 Solve a system of linear equations in three variables
3x-4y+z=11 ①
5y-z=6 ②
4x+2y-3z=12 ③
Solution: ①×4-③×3, we get
-22y+13z=8 ④
② and ④ form a system of equations
5y-z=6
-22y+13z=8
Simple system of linear equations of three variables PPT, the third part: steps to solve the system of linear equations of three variables:
① Use substitution method or addition and subtraction to eliminate an unknown number and obtain a system of linear equations of two variables;
② Solve this system of linear equations of two variables and obtain the values of the two unknowns;
③ Substitute the values of these two unknown numbers into the simpler equation in the original equation to find the value of the third unknown number. Writing these three numbers together is the solution to the system of three-dimensional linear equations.
Keywords: Free download of Hebei Education Edition mathematics PPT courseware for seventh grade volume 2, simple three-dimensional linear equation system PPT download, .PPT format;
For more information about the "Simple System of Linear Equations in Three Variables" PPT courseware, please click the "Simple System of Linear Equations in Three Variables" ppt tag.
"Simple Three-dimensional Linear Equations" PPT:
"Simple Tridimensional Linear Equations" PPT Part 1 content: Content introduction (1) The definition of a tridimensional linear equation contains three unknowns, and the degree of the terms containing the unknowns is 1. An integral equation like this is called a tridimensional linear equation . (2) Three yuan per...
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Update Time: 2024-07-07
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