Techniques and methods of solving equations, methods of solving equations

Remove the denominator, this is the first step in solving the unary equation, the denominator of the unary equation with the denominator must first be denominated, of course, if there is no denominator in the equation, this step is omitted.

Remove the parentheses, after removing the denominator, it is time to complete the removal of the parentheses, if there is a denominator, first remove the denominator and then remove the parentheses, if there are no parentheses, this step can be omitted.

Shifting terms, a step that every unary equation has, is to move the data of the same kind to the same side, and the unknowns to the left of the equal sign.

Merging similar terms, the polynomial in the same kind of terms into a synthesis is called merging similar terms, the coefficients of the same kind of terms are added together as coefficients, the letters and the exponents of the letters are unchanged, it is a critical step in solving the unary equation, it is a very important step, and the law of merging similar terms should be followed when merging similar terms.

Solving an equation is the process of finding out the values of all the unknowns in an equation. The properties of equations are mainly applied to solving equations, and the common methods include estimation method, merging similar terms, shifting terms, formula method, function image method, etc.

The trick of solving equations is that we can solve the results and then substitute the results into the equations, and if the equation can be true, then it means that the results are correct.

When solving a one-dimensional equation, of course, both sides can be added or subtracted at the same time. Well, a number is either multiplied or divided by a number at the same time.

The substitution method is to express the unknown number of one equation in the system of equations with an algebraic formula containing another unknown, and substitute it into another starting equation, which eliminates one unknown and solves it. The substitution method is referred to as the substitution method.

1. Substitution elimination method: turn the coefficient of an unknown number of one of the equations into 1 and substitute it into another equation. For example:

2x+y=9①

5x+3y=21②

Convert to y=9-2x, and then substitute to obtain.

5x+3（9-2x）=21

The x=6 addition, subtraction, and elimination method is to eliminate an unknown number and convert the equation into a one-dimensional equation.

Therefore, it is necessary to make the absolute value of the coefficient of the same unmilled known number equal, and thus cancel it by addition or subtraction.

By adding and subtracting two equations (adding left and left, right and right) to quietly swim around, the method of eliminating an unknown number is as follows. x+y=1

x-y=01)+(2) gives 2x=1

Use the properties of the equation to solve the equation: first of all, we use the equation equation to solve the equation, the first thing we need to understand is that the left and right sides of the equation are added or subtracted from the same number at the same time, the solution of the equation will not change, the left and right sides of the equation are multiplied by a number that is not 0 at the same time, the solution of the equation will not change, and the left and right sides of the equation are divided by a number that is not 0 at the same time, and the solution of the equation will not change. It is more convenient to use the properties of such an equation to solve the equation without errors, and finally the equation can be reduced to a relatively simple formula, and the answer can be directly obtained!

Simplifying the equation: For some more complex equations, it is quite critical to simplify the equation of the equation, so when simplifying, you need to make a simplification of some formulas inside the equation according to the nature of the equation, and finally simplify a two-step equation or a three-step equation into a one-step equation, if you are not too troublesome, you can finally continue to use the properties of the equation to solve the equation, so that you can successfully calculate the answer, and it will not be too difficult. There will be no other problems, and the disintegration is relatively simple.

Addition, subtraction, multiplication and division of the relationship between the parts of the equation to solve the equation: addition, subtraction, multiplication and division as four operations methods, in the equation is bound to exist disturbance, according to the addition, subtraction, multiplication, division of the four aspects of the relationship to solve the equation, in the process of subtraction can use the relationship between the subtracted = difference + subtraction, and multiplication can be solved with a factor = product divided by another factor, where addition and division are the same, but need to be calculated in reverse.

After solving the equation, there is another step that is the most critical, that is, it needs to pass the test, and use the test to verify whether the obtained solution is valid, mainly to bring the obtained solution into an unknown number sought, so as to see if the equation is true, so as to get a solution to the original equation, if the equation cannot be established, it means that the solution is wrong and should be recalculated.

There are many ways to solve equations, different types have different methods, and like practicing martial arts, solving equations cannot be summed up in a word.

If you want to master it well, you still have to practice hard by yourself, and if you are more knowledgeable, you will naturally know how to solve it, and you must know what stage you are in, and what level of practice you should practice, this is my nonsense ......

There are many types of equations, I don't know which one lz is going to solve?

For algebraic equations:

In the case of multivariate equations, a "group" is required to determine the value of the unique unknown. For one-time solutions, there are addition, subtraction, substitution, sequential elimination (commonly used by computers), etc. Fractions, unreasonableness, etc. should be turned into whole formulas and then added and subtracted, substituted, etc.

The last one may be a high-order one. In short, the idea is that there is a pluralistic unity, fractional, irrational integer, high-order and low-order, etc., and finally a unary equation can be solved.

If it is a unary equation, then it should be turned into an integer, the number of times should be clearly distinguished, and the solution should be solved according to the corresponding solution method (formula) of different times. For example:

Unary Equation:

1) If there are parentheses, remove them first.

2) Move Terms: Move the items with unknown numbers to the left, and the constant items to the other right.

3) Merge similar terms: deform the equation into a monomial.

4) Divide the coefficients of the unknowns on both sides of the equation to get the value of the unknowns.

Unary quadratic equations: formula, then prescribe; It is converted to the standard ax square + bx + c = 0, and then the root finding formula is used.

For unary higher-order equations, general equations below the fifth order have formula solutions, and when used, they only need to be converted into the form of general formulas and then substituted for coefficients. Five times or more, only special forms of equations have a formula solution.

In addition, there are also solutions to unary higher-order equations, such as factorization, collocation, and root guessing, but they are only suitable for simple ones.

The above are all exact solutions, and there are many ways to find approximate solutions, such as dichotomy, iterative methods, and so on.

The steps to solve the equation (unary and primary).

Remove the denominator and remove the parentheses.

Move items merge items of the same kind.

The coefficient of unknowns is reduced to 1

4x+2（79-x）=192

Solution: 4x+158-2x=192

4x-2x=192-158

2x=34x=17

The method of solving binary linear equations.

Substitution of the elimination method.

A binary linear equation with simple coefficients is selected to deform and another unknown is represented by an algebraic formula containing one unknown. Substitute the deformed equation into another equation, eliminate an unknown number, and obtain a unary one-dimensional equation (when substituting, it should be noted that the original equation cannot be substituted, but can only be substituted into another equation without deformation, so as to achieve the purpose of elimination.) Solve this unary equation and find the value of the unknown; Substituting the value of the obtained unknown into the deformed equation to find the value of another unknown; The value of two unknowns is the solution of the system of equations by "{"; Finally, check whether the results obtained are correct (substitute into the original equation system for testing, and whether the equation satisfies the left and right).

Addition, subtraction, and subtraction.

Using the basic properties of the equation, the coefficient of an unknown number in the original equation system is reduced to the form of equal or opposite numbers; Then use the basic properties of the equation to add or subtract the two deformed equations, eliminate an unknown number, and obtain a unary equation (be sure to multiply both sides of the equation by the same number, do not multiply only one side, and then use subtraction if the unknown coefficients are equal, and add if the unknown coefficients are opposite to each other); Solve this unary equation and find the value of the unknown; Substituting the value of the obtained unknown into any one of the original equations to find the value of another unknown; The value of two unknowns is the solution of the system of equations by "{"; Finally, check whether the results obtained are correct (substitute into the original equation system for testing, and whether the equation satisfies the left and right).

System of equations 5x+3y=348 , 3x+2y=216 *3=15x+9y=1044, *5=15x+10y=1080 - =y=36

Bring y=36 to get 5x+108=348

Get 5x=240

The solution of the original equation x=48 is x=48 and y=36

Substitution elimination method: The unknown number of one equation in the system of equations is expressed by an algebraic formula containing another unknown and substituted into another equation, which eliminates one unknown and obtains a solution. The substitution method is referred to as the substitution method.

And if you solve it, there are at least a few equations for a few unknowns.

Generally, it is a system of equations.

For example: 2x+y=9

2x-y=-1

Solution: Derive: y=9-2x

Substituting "gets: 2x-(9-2x)=1".

Normal calculations. x= The solution of the system of equations is.

x=y=4