2022 Row test quantity relation: two questions explain the solution of indefinite equation (group) thoroughly

In recent years, the solution of indefinite equation (group) frequently appears in the national Joint examination. In fact, there are two kinds of examination methods, but many students can not distinguish accurately, so that they will be confused when they meet the solution of indefinite equation (group).Can you tell the difference between the two?M community parking charges 5 yuan per day for small vehicles, 8 yuan per day for medium vehicles and 10 yuan per day for large vehicles.On a certain day, there were a total of 20 cars parked in the community, and the total charge was 153 yuan. So how many large cars might there be on that day?A. b. 8 9 c. 10 d. 11.Question 2: If six staplers, four calculators and six folders cost 504 yuan in total, and three staplers, one calculator and three folders cost 207 yuan in total, how much will it cost to buy five staplers, calculator and five folders each?A.465 YUAN B.475 yuan C.485 yuan D.495 YuanOr if you think about it, what’s the essential difference between these two systems?In the first question, the number of cars is unknown, while in the second question, the price is unknown. The difference is that the number of cars in the first question must be an integer, while the number of cars in the second question can not be an integer.(1) The unknown quantity has integer limit When an equation (group) has integer limit to the unknown quantity, the solution of this equation (group) is finite many, can use the substitution method or some numerical characteristics to solve.Taking the first question as an example, the number of small cars, medium cars and large cars can be set as x, y and z, respectively. The equations can be obtained as false, and false can be obtained by simple elimination. It is easy to verify that when z=10, y=1 satisfies the question.So choice C.When there is no integer limit on the unknowns in the equation (group), the solution of the equation (group) is infinitely many, and the method of assignment of zero and the method of coordination coefficient can be used to solve the equations.So let’s talk about these two methods, the first one is zero assignment.If the unit prices of stapler, calculator and folder are x, y and z respectively, then the system of equations is false. Since the unit prices can be non-integer, so there are infinite solutions to the system of equations, but the problem is 5(x+y+z), indicating that x+y+z is a fixed value, so any set of special solutions can be substituted into 5(x+y+z).To simplify the calculation, one of the unknowns can be set to 0 to solve, which is the origin of the method of assigning zero.If x=0, y=45, z=54, so 5(x+y+z)=495.Let’s talk about the second method, the coordination coefficient method, this method is the linear combination of these two equations can find the target formula, observe this equation set, subtract the two equations, 3(x+y+z)=297, so 5(x+y+z)=297÷3×5=495.It should be noted that the two solutions of the second type of indefinite equations have their own advantages and disadvantages. The first method is a little troublesome in the process, but it is simple to operate, and routine operation can be carried out. The second method is simple in the process, but it requires certain observation ability and numerical sensitivity, so people can deal with it flexibly in the examination room.Through the above two examples, I believe that we have a deeper understanding of the indeterminate equation (group) this examination point.More relevant test information please timely pay attention to the official website of Huatu education!

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