Substituting the elimination method of binary equations

Eq. (1) y-x = 21

2) y=4x is (write the idea).

It is known that 2x-3y-4=0,1) If y is expressed in an algebraic formula containing x, then y=( ) writes the idea.

2) If x is expressed in an algebraic formula containing y, then x=( ) writes the idea.

Solution: 1) y-x=21

2) y=4x

then 4x-x=21

3x=21x=7 y=4x7=28

Question (2).

1) If y is expressed in an algebraic formula containing x, then y=( ) writes the idea.

2x-3y-4=0

3y=4-2x

y=(2x-4)/4

2) If x is expressed in an algebraic formula containing y, then x=( ) writes the idea.

2x-3y-4=0

2x=3y+4

x=(3y+4)/2

I hope you can understand it, and I wish you progress in your studies.

1): Substituting the result of 2 into 1, then 1 can be reduced to 4x-x=211) If y is expressed by an algebraic expression containing x, then y=( ).

3y=0+4-2x

y=（4-2x）/3

2) If x is expressed by an algebraic expression containing y, then x=( ).

2x=0+4+3y

x=2+

Question 1: Substituting y=4x into y-x=21 gives 4x-x=21 and gets x=7, and substituting x=7 into y=4x gives y=28

Question 2: (1) Shift the term to get -3y=4-2x

y=(4-2x)/(-3)

Finished, y=(2x-4) 3

2) Move the term to get 2x=4+3y

x=(4+3y)/2

The substitution method of substitution for a system of binary linear equations is:

Treat an equation of one equation in a system of equations as an algebraic equation with another unknown.

Represent it, substitute it into another equation, subtract an unknown, and get a unary equation.

Finally, the solution of the system of equations is obtained.

"Elimination" is the solution of a system of binary linear equations.

The basic idea is to reduce the number of unknowns, so that the multivariate equation is finally transformed into a one-dimensional multiple equation and then solve the unknowns, which is a solution method that reduces the number of unknowns in the equation system from more to less, and solves them one by one.

Basis for solving the equation

1. Shift the term and change the sign: move some terms in the equation from one side of the equation to the other with the previous symbols, and add and subtract, subtract and add, multiply and divide, and divide by multiplication.

2. The basic properties of the equation:

1) Add (or subtract) the same number or the same algebraic formula on both sides of the equation at the same time, and the result is still the equation. It is expressed in letters as: if a=b, c is a number or an algebraic formula.

2) Multiply or divide both sides of the equation by the same non-0 number at the same time, and the result is still the equation. The word Hu is expressed as: if a=b, c is a number or an algebraic formula (not 0).

Steps to solve a system of binary linear equations using the substitution elimination method:

1) Select a relatively simple equation with coefficients from the system of equations, and express one of the unknowns with a formula containing another unknown.

2) Substituting the resulting equation in (1) into another equation and eliminating an unknown.

Zheng Naran 3) solution of the unary one-dimensional equation.

Find the value of an unknown number.

4) Substituting the value of an unknown imaginary number into the equation obtained in (1) to find the value of another unknown number, so as to determine the solution of the system of equations.

Considerations for solving equations1. If there is a denominator, go to the denominator first.

2. If there are parentheses, remove the brackets.

3. If you need to move the item, you will move the item.

4. Merge similar items.

5. The coefficient is reduced to 1 to obtain the value of the unknown.

6. Write "solution" at the beginning.

①2x-y=-1 ②

Substituting into , obtains: 2x-x-2=-1 x=1 Substituting x=1 into , obtains: y=1+2 y=3 x=1 y=3

2x+3y=-8 ②

Result: x=1+y

Substituting y=2y+3y=-8 y=-2 Substituting y=-2 yields:x+2=1 x=-1 x=-1 y=-2

5s-3t=9 ②

Derived: s=7-2t

Substituting 45-10t-3t=9 t=36 13 Substituting t=36 13 yields+2x36 13=7 s=19 13

s=19/13 t=36/13

2x+y+8=0 ②

Result: y=-2x-8

Substituting x=3 yields: 3x+8x+32+1=0 x=3 Substituting x=3 yields: 6+y+8=0 y=-14 x=3 y=-14

3x-4y=2 ②

Result: 3x-6y=-2

Get: 2y=4 y=2

Substituting y=2 yields: 3x-8=2 x=10 3 x=10 3 y=2 (this problem can only be solved by addition, subtraction, and elimination).

4x+3y=-1 ②

Get: 6x=-6 x=-1

Substituting x=-1 yields: -2-3y=-5 y=1 x=-1 y=1 (this problem is also the method of addition, subtraction, and elimination) 7Let A be x and B be y

Column equations: x+y=25

2x+1=y ②

Substituting x+2x+1=25 x=8 Substituting x=8 yields: 8+y=25 y=17 x=8 y=17

Tired to death, plus points].

Solution: Let the ** of the small cake be Y yuan, and the ** of the big cake will be X yuan.

2x+y=6

x+2y=x= of the solution, y=1

Answer: The ** for the big cake is 1 yuan, and the small cake ** is 1 yuan.

Solution: Let A be x and B be y

x+y=25

2y+1=x

The solution is x=17, y=8

Solution: Let the big one be x and the small one be y

2x+y=6 Find: 2x-1x= Substituting 3+y=6 in 1 to get y=3

1x+2y= x= y=3

One. Solution: Obtained from (2): x=13--4y

3) Substitute (3) into (1) to get:

2(13--4y)+3y=16

26-8y+3y=16

5y=--10

y=2 substitute y=2 into (3) to get:

x=13--8=5

So the solution of the original system of equations is: x=5

y=2。Two. Solution: From (2): x=7+y

3) Substitute (3) into (1) to get:

7+y+y=11

2y=4y=2Substituting y=2 into (3) gets:

x=7+2=9

So the solution of the original system of equations is: x=9

y=2。Three. Solution: From (2): x=3--2y

3) Substitute (3) into (1) to get:

3（3--2y)--2y=9

9--6y--2y=9

8y=0y=0 Substituting y=0 into (3) gets:

x=3--0=3

So the solution of the original system of equations is: x=3

y=0。

An unknown is used to represent another unknown and then brought to another equation to construct a unary equation.

Let's start by looking at such a system of binary linear equations, where the two equations are y=......If you replace y in one equation with 4x equivalent to y in two equations, then you can find the value of x. This is the basic idea of substitution.

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So what if there is no such obvious form of y=4x as in the previous question? Looking at the problem in the diagram, what we need to do is to convert one or two formulas to y=......or x=......and then substitute another formula. Therefore, the first step of substitution is often to convert the form of one or two formulas.

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When encountering some more complex formulas, it is also necessary to transform the form first, and this transformation process is actually like a process of solving a primary equation, using one unknown to represent the other unknown.

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In addition to this basic substitution of individual unknowns, some problems can also flexibly use the overall substitution method. This question is shown in the picture. After the two formulas are changed to 2y=1-3x, it is completely possible to substitute 2y as a whole into the formula, so that the first formula becomes 2x-2(1-x)=6.

This saves a step compared to just substituting a y.

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For example, for this question, you can also choose the way of substitution as a whole. Of course, these two examples are relatively simple overall substitution, and there are some problems that can be substituted into the equation as a whole, etc., which need to be experienced and understood.

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Solving binary equations is an important knowledge in middle school, which can be combined with a variety of knowledge, such as the problem on the graph, which integrates the knowledge of complete square roots and absolute values. We can list the binary one-time agenda group one-formula: a+b+5=0, two-formula:

2a-b+1=0。Then by solving the selection.

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Another example is the problem in the figure, which combines the knowledge of similar terms (columnaris: a-b=2, a+b=4). What we need to do is to apply different knowledge flexibly, only then can we be more handy in the exam.

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First, select an equation in the system of binary linear equations, and then use one of the unknowns to represent the other unknown according to the method of solving the equation, so as to obtain a new binary linear equation.

Substituting the obtained new equation into another equation in the binary linear equation system achieves the purpose of elimination, and a unary linear equation is obtained.

Solve the unary equation, substitute the result into the above binary equation, and solve another unknown.