Note: This article is a review of the simple formula of binary for the application of Band 8.
The application of column equation has always been the focus of popular exams and competitions in the next semester of grade eight, and binary linear equation is used to solve application problems. This paper tries to discuss several aspects in the 2005 exam, such as the solution of binary equations in the exam and the examination of application programs.
Solving application problems with column equations
For example, from Beijing to the summer of 2005, in order to save electricity, two measures were often taken: increasing the set temperature of air conditioners and cleaning equipment. For the first time, a hotel raised the setting of two air conditioners A and B by 1℃, and air conditioner B saved 27 degrees every day. Compared with air conditioners A and B, air conditioner B cleans the equipment, which increases the total electricity cost saved every day by1C, and saves the electricity cost by 1. 1 times, while the electricity consumption of air conditioner remains unchanged. Two air conditioners only increase the temperature of 1℃ every day. How many degrees can they save?
Analysis: 4 unknowns: Title Save air-conditioning electricity, raise temperature, after raising temperature, B save air-conditioning electricity, clean equipment, and clean equipment B save air-conditioning electricity. An equal relation of saving air-conditioning electricity-B saving air-conditioning electricity, raising temperature = 27, raising temperature, after cleaning equipment, B saving air-conditioning electricity = 1. 1×, raising air-conditioning electricity, raising temperature, A saving air-conditioning electricity = A saving cleaning equipment, cleaning equipment, A saving air-conditioning electricity+cleaning equipment, B saving electricity = A type. According to the arithmetic relation of the first, second and third, two other unknowns can be expressed, and then according to the relation of the first and fourth arithmetic tables, two linear equations in the two equations can be expressed.
Solution: raise the temperature 1℃, which is a kind of air conditioner and saves X degrees of electricity every day. B the air conditioner saves y degrees of electricity every day.
The same is true for every question:
The solution is:
A: The only temperature rise is 1℃, and the A-type air conditioner saves 207 degrees of electricity every day. Type B air conditioner saves electricity 180 degrees every day.
Second, using linear equations requires the length of line segments.
Example: (Fengtai District, Beijing, 2005) There are 8 identical rectangular tiles on a rectangular floor. Put the tiles together in the data shown in the figure and find the length and width of each tile.
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Analysis: There are two problems, that is, for the length and width of each brick, the length 60 of a rectangle can be an equation. Because the unknowns on the upper and lower sides of rectangle 2 are equal, it can get an equation, thus forming a system of equations.
Solution: Let the length and width of x and y of each brick be respectively, according to the meaning of the problem:
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? The solution is:
A: Each tile is 45 in length and 0/5 in width/kloc.
Double time equation information title
Example 3: (Rizhao City, Shandong Province, 2005) According to the social demand, the municipal government held a water price hearing and decided to adjust the water price from April this year. The price of domestic water for residents is adjusted as follows:
Water consumption (m3) Price (RMB /m3)
The second type is less than 5 cubic meters (including 5 cubic meters)
More than 5 cubic meters x
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In May, we paid 19 yuan and 3 1 yuan to Xiao Lei's family respectively, and the water consumption of Xiao Lei's family was 1.5 times that of Xiao Jing's family.
? The information obtained from your table X.
Analysis: When paying the water fee, I saw Xiaojingjia and Xiao Lei, both of which used more than 5 cubic meters of water, but the water consumption was unknown, so I first set the water consumption of Xiaojingjia in May and Xiao Lei-monthly water consumption 1.5Y cubic meters. This is actually a binary linear equation system, xy and x can be solved, and then the column equation can be solved.
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Fourth, using the binary simple formula of inequality relation
For example, an expressway toll station in Huzhou (2005), m (m > 0) The cost of the train line is waiting to be passed. Assuming no change, the number of cars passing through the toll booth is the same speed every minute (through the toll booth window of each toll booth). If you open the charging window, it will take 20 minutes, maybe the original car is waiting in line, and then all the charges are connected to the car; The window opened these two fees. Originally, it took only 8 minutes to wait in line for the bus, but later the fees for picking up the car passed. If you need to pass the toll, line up in 3 minutes. What should I do if I open at least several toll windows at the same time when picking the car behind me?
Analysis: There are three unknowns in the topic: the car that charges per minute, the traffic per minute, and the need to open the window. There are only two reciprocal relationships, that is, "if you open a toll window, you may have to wait in line for 20 minutes, and all the original cars will be connected to the fare." The original line only takes 8 minutes to get to a car, and then these two fees are added to the open window. All expenses are linked to the name of the car. That is, "all cars waiting in line for tolls within three minutes must get off and pass when they collect tolls." "Therefore, can we list the values of the combination of two linear equations and two time inequalities? Solve two equations of two unknowns, finally generate income inequality, and get the range of salary window number.
Solution: Let each charging window collect traffic by minute? When a car passes through X cars, it needs to open N toll collection windows erected, and all the cars will be charged within three minutes after waiting in line. According to the title "One Germany":
? ①, ② Available: ④
(4) the third generation is also:
∵M & gt； 0, ∴N≥n is the smallest positive integer, ∴N = 5.
A: At least five charging windows have been opened.
Solving function problems by using graphs of linear equations
Example: (Heilongjiang in 2005) Company A and Company B have two rectangular reservoirs, and the water in the reservoirs enters Pool B at the speed of 6 cubic meters per hour. As shown in the figure, the image of the function y(M) × (when) between the water depths of the two reservoirs A and B, combined with the image, answers the following questions:
(1), which are respectively the functional relationship between the water depth y of the two water tanks A and B and the water injection time x;
(2) How to find the water injection depth of A and B reservoirs;
(3) Determine how long the same water injection time is for the two reservoirs A and B..
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Analysis: (1), we can set y a = K 1X+B 1. (o 2), (3,0) substitution solution KL = -23, BL = 2, ∴y +2 Let y =-23X B = K2X+B2. The solutions of (0, 1) and (3, 4) are substituted into = 1, and b2 is set to1∴ k2 of Yb = x+1.
(2) The water depth of two reservoirs, A and B, is actually to pursue the time function of the two places, and at the same time, the two main functions are combined to form the intersection coordinates of a binary linear equation. The equation of this solution is the main function of intersection coordinates. Equation: X = 35. Water injection for 35 hours, the water depth of two reservoirs A and B.
(3) Can we set a new base area of S 1 and B? S2, t hours, two reservoirs A and B have the same volume of water. According to the meaning of the question, 2Sl = 3×6(4- 1) and S2 = 3×6, so Sl is solved as 9:1.
S2 = 6, and because s1(-23t2) 2) = S2 (t+1+0), the solution t = 1. Groups A and B have water storage capacity for one hour.