"System of linear equations in two variables" PPT courseware

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"System of linear equations in two variables" PPT courseware

Question: In a basketball league, each game has a winner. Each team gets 2 points for a win and 1 point for a loss. In order to strive for a better ranking, a team wants to score 40 points in all 22 games. What are the number of wins and losses for this team?

Will you use the linear equations of one variable you have learned to solve this problem?

Solution: If x field is won, then (22-x) field is lost, and the equation can be obtained according to the meaning of the question.

2x+(22-x)×1=40

Solve for x=18

22-18=4

Answer: This team won 18 games and lost only 4 games.

learn new knowledge

An equation containing two unknowns, and the exponents of both unknowns are 1, is called a linear equation of two variables.

Note: Both sides of the equation are integers.

1. Which of the following equations are linear equations of two variables?

① 3x＋xy=1 ② y =3x ③x＋1/y=3;

④ x+y/4=1/6; ⑤ x-2y2=2; ⑥ 3x+4y.

According to the following statements, list the linear equations of two variables:

1. Number A is greater than number B 3. Let number A be x and number B be y;

x-y=3

2. The perimeter of a rectangle is 20cm. Let the length of the rectangle be xcm and the width be ycm;

2(x+y)=20

3. A and B each worked for 5 days and produced a total of 80 parts. Suppose A produces x pieces of parts every day, and B produces y pieces of parts every day.

5x+5y=80

test you

Pencils of type A cost 0.2 yuan each, and pencils of type B cost 0.5 yuan each. Now someone bought x pencils of type A and y pencils of type B, spending a total of 7 yuan.

(1) List the linear equations of two variables with respect to x and y.

0.2X+0.5y=7

(2) If x=5, what is the value of y?

y=12

(3) If 10 pencils of type B were bought, how many pencils of type A were bought?

x=10

Knowledge sorting

The value of the two unknowns that equalizes the values ​​on both sides of a linear equation of two variables is called a solution to the linear equation of two variables.

There are countless solutions to linear equations in two variables.

The common solution of the two equations of a system of linear equations of two variables is called the solution of the system of linear equations of two variables.

Development exercises:

1. In the equation 4x+3y=14, if x and y are equal, then x=______

If x is opposite to y, then x=______; if x is equal to 2 times of y, then x=______y=______

2. "Wu Dalang Selling Cake" is a very interesting ancient poem:

Wu Dalang sells cake skewers all over the street, and the sweet and salty sesame cakes sell quickly. The sweet, salty, and sweet sesame cakes sell out quickly, and the salty, salty, and sweet sesame cakes sell for two or two cents each. If you buy one sweet and salty biscuit each, what is the price of the Wu Dalang cake? Smart classmates, you can Calculate the price of sweet and savory cookies?

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For more information about the "System of Linear Equations in Two Variables" PPT courseware, please click the "System of Linear Equations in Two Variables" ppt tag.

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Update Time: 2024-07-29

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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