"Practical problems and systems of linear equations of two variables" System of linear equations of two variables PPT courseware 4

Description

"Practical problems and systems of linear equations of two variables" System of linear equations of two variables PPT courseware 4

Knowledge review:

A linear equation of two variables: an equation containing two unknowns, and the exponents of the unknowns are all 1, is called a linear equation of two variables.

System of linear equations in two variables: If it consists of two linear equations with two unknowns, then they form a system of linear equations in two variables.

Solution of a linear equation of two variables: the values ​​of the two unknowns that make the left and right sides of the linear equation of two variables equal.

Solution of a system of linear equations in two variables: Generally, the common solution of two equations of a system of linear equations in two variables.

think about it

When Xiao Cong's family goes on a trip, it is estimated that they will need 120 film negatives. There are two types of film in the store: type A with 36 negatives per roll, and type B with 12 negatives per roll. Xiao Cong bought a total of 4 rolls of film, with exactly 120 negatives. How many of the A and B types of films they bought?

knowledge innovation

A certain radio station plans to insert two commercials of 15 seconds and 30 seconds during the 2-minute advertising time during prime time. A 15-second advertisement costs RMB 6,000 per broadcast, and a 30-second advertisement costs RMB 10,000 per broadcast. If each advertisement is required to be played no less than twice, ask:

⑴ How many ways are there to arrange the play times of the two advertisements?

⑵ Which method of broadcasting will the TV station choose to gain the most profit?

It takes 3 hours for a ship to sail 45 kilometers with the current, and 5 hours to sail 65 kilometers against the current. If the speed of the ship in still water is x kilometers/hour, and the speed of the water flow is y�/h, then the values ​​of x and y is ( ) A, X=3, y=2 B, x=14, y=1 C, x=15, y=1 D, x=14, y=2

Exploration 2

According to past statistical data, the ratio of the unit area yield of two crops A and B is 1:1.5. Now we want to plant these two crops on a rectangular land 200m long and 100m wide. How to divide the land into two A rectangle, so that the ratio of the total output of crops A and B is 3:4 (the result is rounded to an integer)?

Analysis: As shown in the figure, a planting plan is: the planting areas of crops A and B are rectangular AEFD and BCFE respectively. Assume AE=xm, BE=ym, and formulate a system of equations based on the quantitative relationship between length and yield involved in the problem.

x+y=200

100x:1.5×100y=3:4

Compare:

The monitor purchased IP cards of the following two denominations for some students, a total of 9 cards, costing 330 yuan. Do you know how many IP cards you bought for each of the two denominations?

1. List the system of linear equations of two variables according to the meaning of the question.

2. Can you tell how many IP cards of each denomination were purchased?

Give it a try:

1. There are 300 two kinds of sleepers in total. The total weight of type A sleepers is 1 ton lighter than the total weight of type B sleepers. If each sleeper of type A weighs 46 kg and type B weighs 28 kg, how many sleepers of each type are there?

2. The vegetable wholesale station has a batch of vegetables distributed to the canteens of the two schools. The 5 times distributed by the canteen of School A is 10kg less than the 6 times distributed by the canteen of School B; the 3 times distributed by the canteen of School A is less than the 6 times distributed by the canteen of School B. The sum of 2 times is 470kg. How much vegetables will each get in the canteens of schools A and B?

give it a try

1. The number of basketballs in the school is 3 less than twice the number of footballs. The ratio of the number of basketballs to the number of footballs is 3:2. How many of these two kinds of balls are there?

2. A well-known question is recorded in the ancient Chinese "Sun Zi Suan Jing": "One hundred horses, one hundred watts, one big horse drags three, and three small horses drag one." How many big horses and how many small horses?

3. There is a ship with a load capacity of 800 tons and a volume of 795 cubic meters. It is now carrying pig iron and cotton. The volume of pig iron per ton is 0.3 cubic meters, and the volume of cotton per ton is 4 cubic meters. Pig iron and cotton How much cotton should be packed in order to make full use of the ship's load capacity and capacity?

4. There are two potions, one with a concentration of 60% and the other with a concentration of 90%. Now we want to prepare 300g of potion with a concentration of 70%. How many grams of each are needed?

The cattle farm originally had 30 cows and 15 calves, which required approximately 675kg of feed per day. A week later, 12 cows and 5 calves were purchased, which required approximately 940kg of feed per day. Breeder Uncle Li estimates that each cow needs about 18 to 20kg of feed per day, and each calf needs about 7 to 8kg of feed per day. Could you please check whether Uncle Li's estimate is correct through calculation?

Analysis: Assume that on average each cow and each calf requires about feed and.

According to the feed consumption in the two situations, find the equality relationship and list the equation system 30x+15y=675 42x+20y=940

Solving this system of equations, we get X=20 Y=5

This means that on average, each cow needs about 20kg of feed per day, and each calf needs about 5kg of feed per day.

Breeder Uncle Li's estimate of the cow's food intake was more accurate, but his estimate of the calf's food intake was on the higher side.

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Update Time: 2024-10-21

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