"Solution of linear equations in three variables" System of linear equations in two variables PPT courseware 3

Description

"Solution of linear equations in three variables" System of linear equations in two variables PPT courseware 3

introduction

Earlier we learned about a system of linear equations in two variables and their solution - the elimination method. For problems with two unknowns, a system of linear equations in two variables can be formulated to solve. In fact, we will encounter many problems with more unknowns in our study and life.

paper money problem

Xiao Ming has 12 banknotes in denominations of 1 yuan, 2 yuan, and 5 yuan, totaling 22 yuan. The number of 1 yuan banknotes is four times the number of 2 yuan banknotes. How many 1 yuan, 2 yuan, and 5 yuan banknotes are there?

Ask a question:

1. How many conditions are there in the question?

2. How many unknown quantities are there in the problem?

3． Can you formulate a system of equations based on equivalence relationships?

Analysis: In this question, we are asked to find three unknowns. We will naturally think of assuming that the 1 yuan, 2 yuan, and 5 yuan banknotes are x pieces, y pieces, and z pieces respectively. According to the meaning of the question, we can get the following three equations :

x+y+z=12,

x+2y+5z=22,

x=4y.

From this, we get the definition of a system of linear equations in three variables:

It contains three different unknowns, and the degree of the unknown term 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＋4z=7 ①

2x＋3y＋z=9 ②

5x－9y＋7z=8 ③

Solution: ②×3+③, we get 11x+10z=35 ④

① and ④ form a system of equations

3x＋4z=7

11x+10z=35

Solving this system of equations, we get X=5 Z=-2

Substituting x=5 and z=-2 into ②, we get y=1/3

Therefore, the solution of the three-dimensional linear equations is X=5 Y=1/3 Z=-2

[Method summary]

According to the characteristics of the system of equations, students summarized this type of system of equations as:

Type 1: There is an expression and the substitution method is used.

Type 2: If a certain dollar is missing, a certain dollar will be eliminated.

Type 3: Same unknown coefficients are the same or opposite, addition, subtraction and elimination method

Activity

The sum of the three numbers A, B, and C is 35. Two times of the number A is 5 greater than the number B. One-third of the number B is equal to one-half of the number C. Find these three numbers.

summary

In this lesson, we learned the solution method of the system of linear equations in three variables. By solving the system of linear equations in three variables, we can further understand the idea of ​​​​eliminating the systems of multivariate equations one by one.

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

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Update Time: 2024-11-22

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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