"Application of linear equations of two variables" PPT

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"Application of linear equations of two variables" PPT

Part One: Review the past and learn the new

List the basic steps for solving word problems using linear equations of one variable.

What is the key to solving word problems using equations?

Find the equivalent relationship

The problem of two horses carrying goods is a question widely circulated in ancient India. There was a conversation between a big horse and a small horse on the way carrying goods as follows.

Dama: "Oh! Carrying so many packages makes me exhausted!"

Xiao Ma: "Are you tired for such a big guy? Give me a pack of what you are carrying, so we can both carry the same amount."

Dama: "Hmph, I'll take one from your back, and my number of packages will be twice that of yours!

Pony: "Really?!"

Based on the conversation between the big horse and the little horse, can you find out how many bags of items the big horse and the little horse are carrying?

talk

What is the equivalence relationship that Xiao Ma mentioned?

Give me a pack of what you're carrying, and we'll both have the same amount.

The number of things carried by the big horse - 1 = the number of things carried by the small horse + 1

I take one from your back and I have twice as many packages as you!

The number of things carried by the big horse + 1 = (the number of things carried by the small horse - 1) × 2

PPT on the application of linear equations of two variables, part 2: analysis of examples

example 1

A fertilizer factory shipped two batches of fertilizer to a certain area. The first batch was filled with 9 train cars and 25 trucks, transporting a total of 640t; the second batch was filled with 12 train cars and 10 trucks, and a total of 760t was transported. On average, how many tons of fertilizer are carried per train car and per truck?

Key to solving the problem

first batch

Total tonnage of 9 train cars + total tonnage of 25 trucks = 640t;

second batch

Total tonnage of 12 train cars + total tonnage of 10 trucks = 760t

Example 2

Last fall, a school had a total enrollment of 500 students in seventh grade and first grade. It plans to increase the enrollment of seventh grade this fall by 20% compared with last year, and the number of first grade students in high school by 15% compared with last year. In this way, the total number of students in the two grades will increase by 18% compared with last year. Find How many students are planned to enroll in seventh grade and first grade in high school this fall?

Key to solving the problem

last fall

The total number of students in seventh grade + the total number of students in high school grade 1 = 500;

this fall

Number of seventh graders + number of first graders = 500 (1+18%)

PPT on the application of linear equations in two variables, part three: cooperative exploration

In order to measure the speed and length of the train when it crosses the bridge, Xiao Ming makes observations next to a railway bridge: it takes 26 seconds for the train to fully cross the bridge, and the time for the entire train to be completely on the bridge is 14 seconds. The length of the bridge is known 1000m. Can you find the speed and length of the train based on the data obtained by Xiao Ming?

think:

⑴. What quantities are involved in the problem?

⑵. Draw a schematic diagram and look for equivalent relationships.

⑶. Use x and y to represent the speed (m/s) and length (m) of the train respectively, and form a system of equations.

⑷. Answer the above questions.

Solution: Let the speed of the train be x m/s and the length be y m. Based on the question

26x=1000+y

14x=1000+y

Solutions have to

x=50

y=300

Answer: The speed of the train is 50 m/s and the length is 300m.

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for seventh grade volume 2, PPT download of application of linear equations in two variables, .PPT format;

For more information about the PPT courseware "Applications of Systems of Linear Equations of Two Variables", please click on the "Applications of Systems of Linear Equations of Two Variables" ppt tag.

"Application of linear equations of two variables" PPT courseware:

The first part of the PPT courseware "Applications of Linear Equations in Two Variables": Basic Quantity Relationships in Travel Problems Distance = Time Speed ​​Time = Distance/Speed ​​Speed ​​= Distance/Time Simultaneous travel in opposite directions Distance = Sum of time speeds Simultaneous travel in the same direction =speed of time..

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Update Time: 2024-10-17

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