"Solution of linear equations in three variables" System of linear equations in two variables PPT courseware 2

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"Solution of linear equations in three variables" System of linear equations in two variables PPT courseware 2

Review the past and learn the new

What is a linear equation of two variables?

An integral equation that contains two unknowns and the terms containing the unknowns are of degree 1 is called a linear equation of two variables.

What is a system of linear equations in two variables?

Containing two unknowns, and the degree of the terms containing unknowns in each equation is 1, such a system of equations is called a system of linear equations of two variables.

Question: 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 4 times the number of 2 yuan banknotes. Find the 1 yuan, 2 yuan, and 5 yuan banknotes. How many of each.

Solution: Let 1 yuan, 2 yuan, and 5 yuan banknotes be x, y, and z pieces respectively.

x+y+z=12

x+2y+5z=22

x=4y

Think: How many unknowns are there in the system of equations?

learn by analogy

Clear concept:

An integral equation that contains three unknowns and the terms containing the unknowns are all of degree 1 is called a linear equation of three variables.

Containing three unknowns, and the degree of the terms containing unknowns in each equation is 1, such a system of equations is called a system of linear equations of three variables.

The idea of ​​​​solving a system of linear equations in three variables is:

(1) Carry out ______ through ______ or ______ to convert the system of linear equations of three variables into the familiar system of linear equations of two variables;

(2) Solve a system of linear equations in two variables;

(3)Finally find the values ​​of ______ unknowns and summarize.

Strike while the iron is hot

If there are three bundles of high-grade millet, two bundles of medium-grade millet, and one bundle of low-grade millet, a total of thirty-nine bushels of millet will be obtained; Four buckets; one bundle of high-grade millet, two bundles of medium-grade millet, and three bundles of low-grade millet, for a total of twenty-nine buckets of millet. How many buckets of each bundle of upper, middle, and lower grade millet can be obtained?

Solution: Suppose there are x, y, and z buckets in a bundle of upper, middle, and lower grades of millet respectively.

According to the question: 3x+2y+z=39

2x+3y+z=34

x+2y+3z=29

The finishing touch

The idea of ​​​​solving word problems of a system of linear equations in three variables is:

(1) Assume three unknowns;

(2) Based on the three equivalence relationships given in the question, list three equations;

(3) Solve the system of linear equations in three variables;

(4) Final inspection.

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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.

"Solution of linear equations in three variables" System of linear equations in two variables PPT courseware 4:

"Solutions to Tridimensional Linear Equations" PPT Courseware for Binary Linear Equations 4 Activity 1 Banknote Problem Xiao Ming has 12 banknotes in denominations of 1 yuan, 2 yuan, and 5 yuan, totaling 22 yuan, of which the number of 1 yuan banknotes is It is 4 times the number of 2 yuan banknotes. Find 1 yuan, 2 yuan, 5 yuan...

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

"Solution of linear equations in three variables" System of linear equations in two variables PPT courseware 3 Introduction Previously we learned about linear equations in two variables and their solution using the elimination method. For problems with two unknowns, a system of linear equations in two variables can be formulated to solve. In fact, in our study...

"Solution of linear equations in three variables" PPT courseware for linear equations in two variables:

"Solution of linear equations in three variables" PPT courseware for linear equations in two variables. The definition of a linear equation in three variables contains three unknowns, and the degree of the terms containing the unknowns is all 1. An integral equation like this is called a linear equation in three variables. How to solve a system of linear equations in three variables? three..

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Update Time: 2024-11-17

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

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