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

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

Activity 1 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?

Solution: Suppose there are x, y, and z banknotes of 1 yuan, 2 yuan, and 5 yuan respectively. According to the meaning of the question, the following three equations can be obtained:

x+y+z=12,

x+2y+5z=22,

x=4y.

System of linear equations in three variables:

Contains three identical unknowns, the degree of the terms containing 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 in three variables.

Observe the coefficients of each unknown number in the following equations. If you use addition and subtraction to solve the system of equations, which element is easier to eliminate first? Why? How to eliminate yuan?

X+y+z=26 3x+4y-z=4

X-y=1 6x-y+3z= - 5

2x-y+z=18 5y+z=11

5x-y=6 5x+2y=5

2y-z=-1 Y-z= - 7

X+2z=12 4z+3x=13

The key to solving a system of three-variable linear equations is elimination, which requires us to carefully observe, analyze, and determine the objects and methods of elimination. This will not only save time, but also help us solve the problem more accurately.

Summarize:

The basic idea of ​​solving a system of linear equations in three variables is: eliminate elements through "substitution" or "addition and subtraction", convert "three variables" into "two variables", so that solving a system of linear equations in three variables is transformed into solving a linear equation in two variables group, and then transformed into solving a linear equation of one variable.

Use the simplest method you think to solve the system of linear equations in three variables:

2x+4y+3z=9

3x-2y+5z=11

5x-6y+7z=13

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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 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" System of linear equations in two variables PPT courseware 2:

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

"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: 2024-07-06

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