"Method of Addition, Subtraction and Elimination—Solution to Systems of Linear Equations in Two Variables" System of Linear Equations in Two Variables PPT Courseware 2

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"Method of Addition, Subtraction and Elimination—Solution to Systems of Linear Equations in Two Variables" System of Linear Equations in Two Variables PPT Courseware 2

Review the past and learn the new

1. What is the basic idea of ​​solving a system of linear equations in two variables?

Basic idea: Elimination: two elements---one element

2. What are the main steps in solving a system of equations using the substitution method?

1. Change---use an algebraic expression containing an unknown number to express another unknown number

2. Generation --- eliminate one element

3. Solution---Find the values ​​of the two unknowns respectively

4. Write---Write the solution of the system of equations

When the coefficients of the same unknown number in two linear equations of two variables are opposite or equal to each other, adding or subtracting both sides of the two equations can eliminate the unknown number and obtain a linear equation of one variable. This method is called addition and subtraction. Elimination method, also known as addition and subtraction method.

Let me tell you:

When using the addition, subtraction and elimination method to solve a system of equations, in the two equations of the system of equations:

(1) If the coefficients of an unknown number are opposites of each other, you can directly add both sides of the two equations to eliminate the unknown number;

(2) If the coefficients of an unknown number are equal, you can directly subtract both sides of the two equations to eliminate the unknown number.

Fill in the blanks

1. It is known that the system of equations x+3y=17①2x-3y=6②two equations

As long as both sides are added separately, the unknown y can be eliminated.

2. It is known that the system of equations 25x-7y=16①25x+6y=10②two equations

As long as both sides are subtracted, the unknown x can be eliminated

Multiple choice questions

1. Use addition and subtraction to solve the system of equations 6x+7y=-19①6x-5y=17②Application ( )

A.①-②Cancel y B.①-②Cancel x

C. ②- ①Eliminate the constant term D. None of the above is correct

2. The system of equations 3x+2y=13①3x-2y=5②The equation obtained after eliminating y is ( )

A.6x=8 B.6x=18 C.6x=5 D.x=18

See if you have mastered it?

Point out whether there are any wrong steps in solving the following system of equations and make corrections:

7x-4y=4 3x-4y=14

5x-4y=-4 5x+4y=2

Solution: ①-②, get Solution: ①-②, get

2x=4-4, -2x=12

x＝0　x＝－6

Solution: ①-②, get Solution: ①＋②, get

2x=4+4, 8x=16

x＝4 x＝2

Thinking: Solving Systems of Equations

3x+4y=16

5x - 6y = 33

Solution: ① ×3: 9x+ 12y = 48

② ×2: 10x - 12y = 66

③+④: 19x = 114, that is, x = 6

Substituting x = 6 into ① we get

18 + 4y = 16 or y = -1/2

The solution of the original system of equations is x = 6 y = -1/2

Enlightenment:

When the coefficients of the unknowns do not have a multiple relationship, the two equations should be transformed at the same time, and the unknown coefficients with smaller coefficients should be selected for elimination.

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Update Time: 2024-11-22

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

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