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Authoritative PPT Summary
"Equations" Equality and Inequality PPT (Solution Set of Equations in Lesson 3)
Part One: Learning Objectives
Be able to use the substitution and elimination method or the addition, subtraction and elimination method to solve systems of linear equations in two variables
Be able to use appropriate elimination methods to solve systems of linear equations in three variables
Flexibly use specific methods to solve "two·one" type and "two·two" type quadratic equations of two variables
Equation PPT, part 2 content: independent learning
Problem guide
Preview the contents of textbook P51-P54 and think about the following questions:
1. What is a system of equations?
2. What is the solution set of a system of equations?
A preliminary exploration of new knowledge
1. equation set
Generally speaking, by combining multiple equations, a system of equations can be obtained.
2. solution set of a system of equations
In a system of equations, the ______ obtained from the solution set of each equation is called the solution set of this system of equations.
■Instructions from famous teachers
When the number of unknowns in the system of equations is greater than the number of equations, the solution set of the system of equations may have infinite elements. At this time, if some of the unknowns are regarded as constants, then other unknowns can often be expressed by these unknowns.
self-test
From the equation system x+m=4, y-3=m, we can get the relationship between x and y ()
A． x+y=1 B. x+y=-1
C. x+y=7 D. x+y=-7
If |x+y-5|+(x-y-9)2=0, then the values of x and y are () respectively
A． -2,7 B. 7,-2
C. -7,2 D. 2,-7
Equation PPT, the third part of the content: interactive teaching and practice
Solutions to systems of linear equations in two variables
Choose an appropriate method to solve the following system of equations:
(1)2x-y=3, ①3x+4y=10.②
(2)x+2y=3, ①3x-4y=4.②
regular method
See how to select coefficients when solving a system of linear equations in two variables
When there are unknown coefficients in the equation that are 1 (or -1), the substitution method can be used to eliminate them directly. Otherwise, observe the coefficients of the same unknown number. When the coefficients are opposites of each other, add and cancel; when the coefficients are equal, subtract and cancel; when the coefficients are neither equal nor opposite to each other, it is necessary to deform the same If the coefficients of the unknown numbers are equal or opposite to each other, then subtract or add to eliminate the variables.
Solution to a system of linear equations in three variables
Angle 1: Solution to general three-dimensional linear equations
Solve the system of equations x+y+z=12, ①x+2y+5z=22, ②x=4y.③
Reflection and induction
Two points to note when solving three-dimensional linear equations using the elimination method
(1) When determining which unknowns to eliminate, we must consider the overall situation. Generally, unknowns that can make the calculation amount relatively small after elimination are selected.
(2) The unknown numbers eliminated must be the same unknown number, otherwise the purpose of elimination will not be achieved.
Equation PPT, Part 4: Feedback on Compliance
1. Solve the following system of equations:
(1)2x+5y=16, ①8x-7y=10; ②
(2)x+1=5(y+2), x-32=y+63.
2. Solve the system of equations 3x-y+z=4, ①x+y+z=6, 2x+3y-z=12. ③
3． Solve the system of equations x2-4y2+x+3y-1=0, ①2x-y-1=0. ②
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For more information about the PPT courseware "Equations and Inequalities, Sets of Solutions to Systems of Equations," please click on the Equations and Inequalities ppt Set of Solutions to Systems of Equations ppt tab.
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