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Calculation of binary linear equations in seventh grade mathematics
1. Solve the equation by adding, subtracting and eliminating elements, which is obtained by ①× 2-②.

2. In equation = 5, it is contained by algebraic expression, which is expressed as: = When = 3, =.

3. In the algebraic expression, when =-2 and = 1, its value is 1, then =; When = 2, =-3, the value of the algebraic expression is.

4. Assuming that the equation has the same solution as, then =, =.

5. If, then =, =.

6. There is a two-digit number and the sum of its two numbers is 1 1. If the single digit of this two-digit number is reversed with the ten-digit number, the new number is 63 larger than the original number. If the single digit of the original two digits is 0 and the decimal digit is 0, then the original two digits are represented by algebra, and the equations are obtained according to the meaning of the question.

7. If = 3 and = 2 are solutions of the equation, then =.

8. If it is the solution of the equation about sum, then =.

9, known, the value is.

Second, multiple-choice questions:

10, in the system of equations,,,, is a binary linear system of equations ().

a,2 B,3 C,4 D,5。

1 1. If it is a similar project, the value of is ().

a 、=-3、=2 B 、=2、=-3

c 、=-2、=3 D 、=3、=-2

12 is called the solution of the equations, so the relationship between them is ().

A, B, C, D,

13, if the binary linear equation has a common * * * solution, then the value of ().

a、3 B、-3 C、-4 D、4

14. If the binary linear equation has a positive integer solution, the value of should be ().

A, positive odd number b, positive even number c, positive odd number or positive even number d, 0

15, if the solution of the equations satisfies > 0, the value range of is ().

a 、- 1 D 、> 1

16, the equation is a binary linear equation, then the value is ().

a、≠0 B 、≠- 1 C、≠ 1 D、≠2

17, when solving the equation, a student gets it wrong, but the correct solution is then, and the value of is ().

A, uncertain b, = 4, = 5, =-2.

C, uncertain, =-2 d, = 4, = 7, = 2.

18. At that time, the value of the algebraic formula was 6, so the value of this formula at that time was ().

a、6 B、-4 C、5 D、 1

19, let's assume that the distance between towns A and B is 1000 meters. A starts from town A and town B at the same time and travels in the opposite direction. The driving speeds of A and B are 1000 m/h and 1000 m/h respectively, and they meet 30 minutes after departure. (2) A immediately returned to town B, and it took another 30 minutes to catch up with B; When A caught up with B, they were still 4 kilometers away from a town. Seek … According to the meaning of the question and condition ③, each of the four students draws the following third equation, and the wrong one is ().

A, B, C, D,

Four, column equation (group) to solve application problems:

22. Wang Chengbao contracted 25 mu of land and replanted eggplant and tomatoes in the greenhouse this spring, which cost 44,000 yuan. Among them, planting eggplant costs 1700 yuan per mu, and the net profit is 2400 yuan; The cost of planting tomatoes per mu 1800 yuan, and the net profit is 2600 yuan. Ask uncle Wang how much is the net profit?

23. In social practice, students A, B and C of a school investigated the traffic flow (the number of cars passing through observation points every hour) in the peak hours of the Second Ring Road, the Third Ring Road and the Fourth Ring Road in Beijing. The three students reported the traffic volume during the rush hour, as follows:

Some students said, "Second Ring Road traffic 10000 vehicles/hour";

Student B said: "The traffic volume of the Fourth Ring Road is 2000 more than that of the Third Ring Road";

Classmate C said: "The traffic flow difference between the Third Ring Road and the Fourth Ring Road is twice that of the Second Ring Road";

According to the information provided by them, please find out the traffic volume during the peak hours of the Third Ring Road and the Fourth Ring Road.

Verb (abbreviation of verb) synthesis;

24. The solution of the known binary linear equations satisfies the binary linear equations and obtains the value.

25. A classmate found in supermarkets A and B that the unit price of his favorite walkman was the same, and so was the unit price of his schoolbag. The sum of the unit price of the walkman and the schoolbag is 452 yuan, and the unit price of the walkman is four times less than that of the schoolbag. 8 yuan.

(1) What is the unit price of the walkman and schoolbag that students like?

(2) One day, the students went out to the street just in time for the merchant's promotion, and all the goods in Supermarket A were 20% off. Supermarket B returned the shopping vouchers to 30 yuan for sale when the total shopping cost was more than 100 yuan (less than 100 yuan, which is common for shopping vouchers), but he only brought 400 yuan money. If he only bought these two things in one supermarket, can you explain which one he would choose to buy? If both companies can choose, which one is more economical to buy?

Reference answer:

First, fill in the blanks:

1、; 2、, 16; 3、=-2,-7; 4、=,= 12; 5、=,=; 6、,; 7、=7; 8、-43; 9、0

Second, multiple-choice questions:

answer

B

B

D

D

A

C

C

B

B

A

Four, column equation to solve application problems:

22. Solution: Suppose Uncle Wang planted 100 mu of eggplant and 100 mu of tomatoes.

Solution:

∴ Wang Dabo * * * Net profit: 2400×10+2600×15 = 6300 (yuan).

A: Uncle Wang netted 6300 yuan.

23. Option 1: Let the traffic flow of the Third Ring Road be one car per hour during peak hours, and the traffic flow of the Fourth Ring Road be one car per hour during peak hours.

Solving this equation is = 1 1000.

∴= 13000

A: During peak hours, the traffic flow of the Third Ring Road is 1 1000 vehicles/hour, and that of the Fourth Ring Road is 13000 vehicles/hour.

Option 2: Let the traffic flow of the Third Ring Road and the Fourth Ring Road be vehicles per hour during peak hours. According to the meaning of the question:

solve

A: During peak hours, the traffic flow of the Third Ring Road is 1 1000 vehicles/hour, and that of the Fourth Ring Road is 13000 vehicles/hour.

Verb (abbreviation of verb) combination;

24. Solution: Get the ternary linear equations from the meaning of the problem:

simplify

①+②-③ Get:

② ② ②× 2-①× 3 ④ Get: ⑤

From ④ ⑤: ⅷ

25. Solution: (1) Solution 1: If the unit price of the schoolbag is yuan, then the unit price of the walkman is yuan.

According to the meaning of the question, you must

To solve this equation, you must

A: The unit price of this student's favorite walkman is 360 yuan, and the unit price of schoolbag is 92 yuan.

Option 2: Set the unit price of schoolbag to RMB, and the unit price of walkman to RMB.

According to the meaning of the question, you must

To solve this system of equations, you must

A: The unit price of this student's favorite walkman is 360 yuan, and the unit price of schoolbag is 92 yuan.

(2) Buying a walkman and a schoolbag in Supermarket A requires cash:

(yuan)

Because 36 1.6 < 400, you can choose supermarket a to buy it.

In supermarket B, you can spend 360 yuan cash to buy a walkman, and then use the 90 yuan coupons you get and 2 yuan cash to buy a schoolbag, which costs a total of * * *:

360+2 = 362 (yuan)

Because 362 < 400, you can also choose to buy it in supermarket B.

Because it is 362 > 36 1.6, it is more economical to buy it in supermarket a.

References:

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