1. In the following equations, (d) is a system of binary linear equations.

(A) (B) (C) (D)

2. If the equation has a set of solutions, its value is (a).

(A) 1 (B)— 1 (C)0 (D)2。

3.a+b= (B) If the solution of the equation is known.

(a) Articles 2 (b) to 2 (c) and 4 (d) to 4

4. If it is a binary linear equation, then the values of a and b are (c) respectively.

(A) 1，0 (B)0，- 1 (C)2. 1 (D)2，-3

5. Place a pair of triangle wrenches as shown in figure 1, and the degree of ∠ 1 is 50 greater than that of ∠2. If ∠ 1 = x ∠ 2 = y, the system of equations can be obtained as (d).

A B C D

6. The distance between Party A and Party B is 360 kilometers. It takes 18 hours for a ship to travel between Party A and Party B, and 24 hours for sailing against the current. If the speed of the ship in still water is X km/h and the current speed is Y km/h, then the correct one in the following equation is (a).

A.B. C. D。

7. If it is the solution of the equations, the analytical formula of the linear function y=mx+n is (d).

A.y=-x+2 B.y=x-2 C.y=-x-2 D.y=x+2

8. If the image of the function y = ax-3 and the image of the function y=bx+4 intersect at a point on the X axis, then a: b is equal to (d).

A.-4∶3 b . 4∶3 c .(-3)∶4d . 3∶4

9. If the sum of the solutions x and y of the system of equations is 2, the value of a is (b).

A.-4b 4c 0d Any number

10. There is an ancient fable: donkeys and mules walk together. They carry different bags of goods, each with the same weight. The donkey complained that the burden was too heavy. The mule said, "Why are you complaining?" If you give me a bag, I will bear twice your weight; If I give you a bag, we will bring the same amount! "So the number of bags of goods originally carried by this donkey is (A)

A.5 B.6 C.7 D.8

Second, fill it out carefully!

1. If the solution of a binary linear equation is 0, then the equation can be _ _ _ _. Just write one.

2. Please write that the positive integer solution of the equation x+2y=7 is _ _ _ _ _.

3. Suppose the solution of the equation is, and the value of is _ _ _ _ _ _.

4. Write the binary linear equations with the solution of _ _ _ _ _ _ _.

5. If the sum of equations about X and Y has the same solution, then A = _ _ _ _ _ _, and B = _ _ _ _ _.

6. The image composed of all points whose coordinates are the solutions of binary linear equations is also the image of linear functions.

7. As shown in the figure, if the image of the sum of functions is known to intersect at point P, then according to the image, the solution of the binary linear equations is.

8. The sum of ten digits and single digits of two digits is 8. If you add 18 to this two-digit number, it is exactly equal to the new two-digit number formed by the exchange of ten digits and single digits of this two-digit number, then the original two-digit number is _ _ _ _ _ _.

9. Company A buys two kinds of pure water, A and B, 250 yuan, in which A water is 8 yuan per barrel, B water is 6 yuan per barrel, and the number of barrels of B water is 75% of A water. If water A is X bucket and water B is Y bucket, the equation can be listed as _ _ _ _ _.

10. A school arranges dormitories for seventh-grade students. If there are five people in each dormitory, four people can't live in it. If there are 6 people in each room, then there are only 4 people in one room and two dormitories are empty. If the number of people is x and the number of rooms is y, the countable equation is _ _ _ _ _ _.

Third, do it with your heart!

1. Known binary linear equation: (1); (2) ; (3) ;

Please choose two equations you like from these three equations to form an equation group and find the solution of this equation group;

2. Knowing that real numbers A and B satisfy, find the value of algebraic expression.

3. As shown in Figure 5, some algebraic sums are filled in a 3×3 square.

(1) In Figure (3), the sum of three numbers in each row, column and diagonal is equal. Please find the values of x and y;

(2) Fill in the other six numbers that satisfy (1) in the box in Figure (4).

4. Before Class 3, Grade 8 held the final summary commendation meeting, the class teacher arranged for Li Xiaobo, the monitor, to go to the store to buy prizes. The following is a conversation between Li Xiaopo and the shop assistant:

Li Xiaobo: Hello, Aunt!

Shop assistant: Hello, classmate. what can I do for you?

Li Xiaobo: I only have 100 yuan. Please arrange for me to buy 10 and 15 notebooks.

Shop assistant: OK, each pen is more expensive than each notebook. 2 yuan, here is your money, 5 yuan. Please count. Goodbye.

According to this conversation, can you work out the unit price of a pen and a notebook?

5. the solution of the equation of x and y is also the solution of the equation of finding the value of m.

6. When doing the puzzle, Xiao Ming found that eight rectangles of the same size can just be put together into a big rectangle, as shown in Figure 5. Xiaohong saw it and said, "I'll try." As a result, Xiaohong put eight pieces together to make a square, as shown in Figure 6. Why did he leave a hole in the middle, which happened to be a small square with a side length of 2mm! Can you work out the length and width of each rectangle?

7. A university has five big restaurants and two small restaurants. According to the test, 1 a big restaurant and two small restaurants are open at the same time, which can provide meals for 1680 students. At the same time, two large restaurants and 1 small restaurant are open for 2280 students to eat.

(1) Find out how many students 1 big restaurant and 1 small restaurant can eat;

(2) If 7 restaurants are open at the same time, can they serve 5,300 students in the whole school? Please explain the reason.

Tickets for the 2008 Beijing Olympic Games began to be booked by the public. The following table shows the ticket prices of several ball games published on the official ticketing website of the Olympic Games. Fan Xiaoli spent 8000 yuan to buy tickets for the following activities.

Ticket price of competition events (yuan/field)

Men's Basketball Team 1000

Football 800

Table tennis 500

(1) If all the funds are used to book tickets for men's basketball and table tennis *** 10, how many tickets for men's basketball and table tennis have been booked? (2) Xiao Li wants to reserve three tickets for men's basketball, football and table tennis with all the funds *** 10. Can his idea come true? Please explain the reason.

Reference answer: 1. DABCD，ADDBA；

Second, 1. The solution is not unique. For example, 2x-y = 5 or 3x+y = 5, or x-4y = 6 and so on. 2. You can use one or both of them; 3.6; 4. cuddling: because x replaces 1 and y replaces 2, the equations are obtained; 5.2, 1; 6.； 7.； 8.35; 9.； 10.；

3. 1. Select (1) and (2) to form the equation.

( 1)+(2):

Substituting (1) gives: ∴ The solution of the original equations is

Note: The solution of the equation group composed of (1) and (3) is, and the solution of the equation group composed of (2) and (3) is

2. solution: get the solution from the meaning of the question, so =;

3. Solution: (1) can be obtained from known conditions: solution.

(2) The table shown in Figure 6 can be obtained from (1).

4. Solution: X yuan for each pen and Y yuan for each notebook. According to the meaning of the question, you get

Solve this system of equations and get

A: Every pen is 5 yuan, and every notebook is 3 yuan.

5. Solution: From the meaning of the question, it can be seen that the solution of the equation group is also valid, and the equation group contains the undetermined coefficient m. If the solution of the equation group is expressed by the algebraic expression of m and substituted into the equation, the problem will be transformed into a linear equation about m, and the value of m can be obtained.

Get a solution

substitution

solve

Substitution equation

Sort it out and get a solution.

6. Solution: Let the length of the rectangle be xmm and the width be ymm. According to the meaning of the question, you can get

The answer after sorting out is: the length of these small rectangles is 10mm and the width is 6 mm.

7. Solution: (1) Set 1 student canteen, 1 student Sashido. According to the meaning of the problem, we can solve this system of equations and get.

A: There are 960 students in 1 big restaurant and 360 students in 1 small restaurant.

(2) because,

So if you open seven restaurants at the same time, you can serve 5300 students in the whole school.

8. Solution: (1) Book X tickets for men's basketball and Y tickets for table tennis.

Get a solution from the meaning of the problem

A: Six tickets for men's basketball and four tickets for table tennis.

(2) Yes. The reasons are as follows: If Xiao Li reserves X tickets for men's basketball and Y tickets for football, then the tickets for table tennis are (10-x-y).

According to the question, it means1000x+800y+500 (10-x-y) = 8000. The arrangement is 5x+3y=30, y=.

∵x, y are positive integers, ∴ when x=3, y=5, ∴ 10-x-y = 2.

Book three tickets for men's basketball, five tickets for football and two tickets for table tennis. Xiao Li's idea can come true.

Alternative questions:

1. Among the following equations, the binary linear equation is (b).

(A)xy = 1(B)y = 3x- 1(C)x+= 2(D)x2+y-3 = 0

2. Is the solution of the equation ax-y=3, then the value of a is (a).

a . 5 B- 5 c . 2d . 1

3. The following equation: ① xy-3z = 4; ②+2y = 3； ③x+y+= 0； ④5(x- 1)= 6(y-2)； ⑤x+ =2 is a binary linear equation with (C )A, 1 b, 2 c, 3 d, 4.

4. If 2x+5y+4z = 0 and 4x+y+2z = 0, the value of x+y+z is equal to (a).

A, 0 B, 1 C, 2 D, can't be found.

5. The solution of the equation is (c)

A.B. C. D。

6. The logo of the International Congress of Mathematicians held in Beijing in August 2002 is as shown in the figure. It is a big square consisting of four identical right-angled triangles and a small square in the middle. If the area of a big square is 13 and the area of a small square is 1, then the long right-angled side of a right-angled triangle is A and the short right-angled side is B, then the value of A3+B4 is (c).

35 BC to 43 BC

7. Please write a set of binary linear equations with X and Y as unknowns, and satisfy the following two conditions at the same time: ① It consists of two binary linear equations; (2) The solution of the equation is as follows, and the equation can be _ _ _ _ _ _. 7.；

8. Solving equations

8. Solution: The equations are transformed into x=3.

You get 4y=2, so the solution of the equation is

9. If it is the solution of binary linear equation, write the binary linear equation that satisfies the meaning of the question and write the integer solution of this equation.

9.。 Find the value of y when x= 1, 2, 3, 4, 5, 6, 7.

10. Pave a large rectangular floor with eight identical rectangular floor tiles. See Figure 2 for the layout of floor tiles and related data. Find out the length and width of each floor tile.

(Figure 2)

10. solution: let the length and width of each floor tile be xcm and ycm respectively.

Answer: The length and width of each floor tile are 45cm and 15cm respectively.

1 1. Li Minghe and Wang Yun go from A and B respectively. If you start at the same time, meet in 80 minutes; If Li Ming leaves Wang Yun in 60 minutes, then 40 minutes later, the two meet. How many hours does it take for Li Minghe and Wang Yun to go to AB alone?

1 1. Suppose the distance between A and B is S km, and the speed of Wang Yun, Li Minghe is X km/min and Y km/min respectively, then according to the meaning of the question, it is concluded that it takes time for Li Ming to walk this distance alone = 120 (minutes), and it takes time for Wang Yun to walk this distance alone = 240.

It shows that we should pay attention to the unity of units when solving, and it is more convenient to solve if the unit of speed is km/min.

12. It is known that the equation (2A-7B) x+(3A-8B)=8x+ 10 is true for all numbers x, so the values of a and b are found.

12. solution: there is a solution from the meaning of the question: that is, the values of a and b are,

13. One day, a vegetable business owner bought 40 kilograms of tomatoes and beans from the wholesale vegetable market with 60 yuan money and sold them in the vegetable market. The wholesale and retail prices of tomatoes and beans on this day are shown in the following table:

Tomatoes and beans

Wholesale price (unit: yuan/kg) 1.2 1.6

Retail price (unit: yuan/kg) 1.8 2.5

Q: How much can he earn by selling these tomatoes and beans that day?

13. Solution: Let the wholesale tomatoes xkg and beans ykg, then according to the meaning of the problem, we can solve this set of equations, so when x = 10, y = 30, 0.6x+0.9y = 0.6x10+0.9× 30 = 33.

Answer: Vegetable business owners use 60 yuan money to wholesale ***40kg tomatoes and beans from the vegetable market to the vegetable market. After selling these tomatoes and beans that day, he can make money in 33 yuan.

14. It is known that a computer company has three models of computers, A, B and C, and their prices are A 6000 yuan, B 4000 yuan and 2500 yuan respectively. Dongpo Middle School in our city plans to spend 100500 yuan to buy 36 computers of two different models from this computer company. Please design several different purchasing schemes for the school to choose from and explain the reasons.