"Solving a system of linear equations in two variables" A system of linear equations in two variables PPT courseware 4

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"Solving a system of linear equations in two variables" A system of linear equations in two variables PPT courseware 4

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What are the characteristics of the previous systems of equations? What is the basic idea of ​​​​solving such systems of equations? What are the main steps?

Features: The absolute value of the coefficient of a certain unknown number is the same

Basic idea: addition, subtraction and elimination of elements

Main steps: two-element - one-element

Solve the following system of linear equations in two variables

2x+3y=12

3x+4y=17

Solution: ①×3, get: 6x+9y=36.③

②×2, get: 6x+8y=34. ④

③-④, get: y=2.

Substituting y=2 into ①, we get: x=3.

So the solution to the original system of equations is x=3 y=2

(1) The basic idea of ​​adding, subtracting and eliminating elements to solve a system of linear equations of two variables is still "elimination".

(2) The general steps for solving a system of linear equations in two variables by adding, subtracting and eliminating elements are:

①Deform to make the absolute value of the coefficient of an unknown number equal.

②Add and subtract elements to obtain a linear equation of one element.

③Solve linear equations of one variable.

④ Substitute the value of another unknown number to obtain the solution of the system of equations.

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Update Time: 2024-10-01

This template belongs to Mathematics courseware Beijing Normal University eighth grade first volume mathematics industry PPT template

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