"Review" System of linear equations in two variables PPT courseware

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"Review" System of linear equations in two variables PPT courseware

Related concepts

1. A linear equation of two variables: After simplification, there are only two unknowns, and the integer equation of the unknown terms is all 1, and the coefficients are not 0, is called a linear equation of two variables.

2. Solution to a linear equation of two variables: The value of the two unknowns that equalizes the values ​​on both sides of the linear equation of two variables is called the solution of the linear equation of two variables.

3. System of linear equations in two variables: A system of equations consisting of two linear equations with two unknowns is called a system of linear equations in two variables.

4. Solution to a system of linear equations of two variables: The common solution to each equation in a system of linear equations of two variables is called the solution to a system of linear equations of two variables.

5. Solution to system of equations: basic idea or idea—elimination

Commonly used methods——substitution and addition and subtraction

Determine which solution method to use based on the coefficient characteristics of the unknowns in the equation.

Steps to solve a system of linear equations in two variables using the substitution method:

(1). Find an expression: Select an equation with relatively simple coefficients from the system of equations, and express an unknown number in this equation, such as y, with an algebraic expression containing x;

(2). Substitute this algebraic expression containing x into another equation, eliminate y, and obtain a linear equation of one variable about x;

(3). Solve the linear equation of one variable and find the value of x;

(4). Then substitute the calculated value of x into the deformed equation to find the value of y.

Steps to solve a system of linear equations in two variables using addition and subtraction:

(1). Use the properties of equality to multiply both sides of one or two equations by appropriate numbers, and transform the coefficient of an unknown number of the two equations so that its absolute value is equal;

(2). Add or subtract both sides of the two equations after the transformation coefficients, eliminate an unknown number, and obtain a linear equation of one variable;

(3). Solve this linear equation of one variable and find the value of an unknown number;

(4). Substitute the unknown value you are seeking into a simpler equation in the system of equations to find the other unknown number, thereby obtaining the solution to the equation.

Itinerary questions:

1. Encounter problem: A’s distance + B’s distance = total distance

(circular track): A’s distance + B’s distance = one lap length

2. Follow up the problem: the distance of the fast person - the distance of the slow person = the original distance

(Circular track): The distance of the fastest person - the distance of the slow person = the length of one lap

3. Sequential and inverse problems: Sequential speed = static speed + water (wind) speed

Reverse speed = static speed - water (wind) speed

Chart issues

1. A certain school currently has 35% of material A and 29% of material B to produce two types of handicrafts, A and B. The materials used are as follows:

(1) How many pieces of crafts A and B can be made using these materials?

(2) If each kilogram of materials A and B costs 8 yuan and 10 yuan respectively, how much does it cost to make two types of handicrafts, A and B?

The problem of constant total quantity

1. After joining the WTO, various domestic automobile companies launched a price war, car prices dropped significantly, and some models of cars were in short supply. A car manufacturer has accepted an order to produce a batch of cars within a specified date. If 35 cars are produced every day, there will be a shortfall of 10 cars to complete the task. If 40 cars are produced every day, the task can be completed half a day ahead of schedule. What are the order requirements? How many cars and what days are required?

Sales questions:

List price × discount = selling price

Selling price - purchase price = profit

Profit rate = profit / purchase price = selling price - purchase price / purchase price

Supporting issues

For example: A certain workshop can produce 120 parts of type A, 100 parts of type B, or 200 parts of type C every day. Only 3, 2, and 1 of the three types of parts A, B, and C can be used to make a set. To produce the largest number of complete sets of products within 30 days, how many days should each of the three parts A, B, and C be produced?

Special training on linear equations and linear functions of two variables:

1. It is known that the graphs of functions y=2x-1 and y=3x+2 intersect at point P, then the coordinates of point P are ( ).

(A) (-7, -3) (B) (3, -7) (C) (-3, -7) (D) (-3, 7)

2. It is known that the straight line y=-1/2x+b and the straight line y=x intersect at point P, then the values ​​of P are ( ).

(A) 2,3 (B) 3,2 (C)-1/2,2 (D) -1/2,3

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For more information about the "System of Linear Equations in Two Variables" PPT courseware, please click the "System of Linear Equations in Two Variables" ppt tag.

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Update Time: 2024-10-20

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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