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"Solution of linear equations in two variables by substitution method" PPT courseware for linear equations in two variables
1. Review questions
1. What is a linear equation of two variables? System of linear equations in two variables? Solution to a system of linear equations in two variables?
2. What is the method for testing the solution of a system of linear equations in two variables?
3. Which of the following equations are linear equations of two variables ( )
A.xy-7=1 B.2x-1=3y+1 C.4x-5y=3x-5y D.2x+3x+4y=6
4. In the linear equation of two variables 3X-5Y=9, when X=0, the value of Y is _______
5. It is known that the linear equation of two variables is 2X+3Y+5=0
⑴Use X to represent Y ⑵Use Y to represent X
2. Newly taught content
1 Definition: Express an unknown number of an equation in a system of equations with an algebraic expression containing another unknown number, substitute it into another equation, eliminate one unknown number, obtain a linear equation of one variable, and finally find the solution of the system of equations. This method is called substitution elimination method, or substitution method for short.
The idea of solving the problem of a system of linear equations in two variables is:
System of linear equations of two variables, substitution, elimination, linear equation of one variable
2. Steps
⑴ Equation deformation: Express an unknown number of one of the equations with an algebraic expression containing another unknown number (X=aY+b or Y=aX+b)
⑵ Substitution and elimination: Substitute the deformed equation into another equation, eliminate an unknown, and transform the system of linear equations of two variables into a linear equation of one variable.
⑶Equation solving: Solve the solution of the linear equation of one variable, then substitute it into the original equation or the transformed equation to find the solution of another unknown number, and finally obtain the solution of the system of equations.
⑷Oral arithmetic test.
3. Consolidate practice
⑴Equation 5X-3Y=7, deformed to get X=_______, Y=________.
⑵Solve the system of equations Y=X-3 ① 2X+3Y=6 ② ____ should be eliminated, and _____ can be substituted into _____.
⑶The common solution of equation Y=2X-3 and equation 3X+2Y=1 is X=_____ Y=_____
4. Summary:
⑴The key to solving a system of linear equations of two variables is "elimination", that is, eliminating an unknown number to transform the "two variables" into "one variable".
⑵ Pay attention to the problem-solving steps.
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