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"Method of Addition, Subtraction and Elimination - Solution to System of Linear Equations in Two Variables" PPT courseware for system of linear equations in two variables
Review the past and learn the new
1. What is the basic idea of solving a system of linear equations in two variables?
Basic idea: Elimination: two elements---one element
2. What are the main steps in solving a system of equations using the substitution method?
1. Change---use an algebraic expression containing an unknown number to express another unknown number
2. Generation --- eliminate one element
3. Solution---Find the values of the two unknowns respectively
4. Write---Write the solution of the system of equations
Understand the rules and reveal the essence
When the coefficients of the same unknown number in two linear equations of two variables are opposite or equal, adding or subtracting both sides of the two equations can eliminate the unknown number and obtain a linear equation of one variable. This method is called the addition, subtraction, and elimination method. , referred to as addition and subtraction.
learn by analogy
Example 1. Solving a system of equations
2x-5y=7 ①
2x+3y=-1 ②
Analysis: Observe the two equations in the system of equations. The coefficients of the unknown x are equal, both are 2. By subtracting both sides of the two equations, you can eliminate the unknown x and obtain a linear equation of one variable.
Use new knowledge to expand innovation
3x-2y= -1 ①
6x+7y=9 ②
Analysis: 1. What conditions must be met to solve a system of linear equations in two variables using addition and subtraction?
2. Can this system of equations be eliminated directly by addition and subtraction?
Summary: What did you gain from studying this lesson?
1. Addition and subtraction method: When the coefficients of the same unknown number in two linear equations of two variables are opposite or equal, add or subtract the two sides of the two equations respectively to eliminate the unknown and obtain a linear equation of one variable. This is This method is called the addition, subtraction, and elimination method.
2. The main steps of solving the system of equations by adding, subtracting and eliminating elements:
Change---use an algebraic expression containing an unknown number to express another unknown number
Generation---Eliminate one element
Solution---Find the values of the two unknowns respectively
Write---Write the solution to the system of equations
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