"System of linear equations in two variables" PPT courseware 2

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"System of linear equations in two variables" PPT courseware 2

In the basketball league, every 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?

think

What conditions are included in the above question that must be met at the same time? Suppose the number of winning games is x and the number of losing games is y. Can you express these conditions using equations?

As we know from the question, the question contains two conditions that must be met at the same time:

Number of wins + number of losses = total number of games

Points for wins + points for losses = total points

observe

x－y＝2 x+y=22

x+1＝2(y－1) 2x+y=40

What do the equations listed above have in common?

Every equation contains 2 unknowns;

The exponents of unknown numbers are all 1.

linear equation of two variables

Among the above equations, each equation contains two unknowns (x and y), and the exponents of the unknowns are all 1. Equations like this are called linear equations of two variables.

Which of the following equations are linear equations in two variables?

(1) x+y+z=9 (2) x=6

(3) 2x+6y=14 (4) xy+y=7

(5) 7x+6y+4=16 (6) x²+y=6

Explore

(1) Does x = 6, y = 2 fit the equation x + y = 8?

What about x = 5 and y = 3?

Can you find other x, y values ​​that fit the equation x + y = 8?

(2) Does x = 5, y = 3 fit the equation 5x + 3y = 34? What about x = 2, y = 8?

(3) Can you find a set of x, y values ​​that simultaneously fit the equations x + y = 8 and 5x + 3y = 34?

Consolidation exercises

1. Which of the following equations is a linear equation of two variables ( )

A.x=3y B.2x+y=3z

C.x²+x-y=0 D.3x+2=5

2. It is known that the linear equation of two variables is 3x-2y=9. If y=0, then x=____.

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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: 2024-10-15

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

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