Addition, subtraction, multiplication and division is one of the important methods to solve equations in high school mathematics. Its main idea is to add or subtract multiple equations containing unknowns to eliminate them, so as to get an equation containing only one unknown, and then get the value of the unknown.

1. Basic concepts

Addition, subtraction and elimination are also called elimination method or elimination method. Its basic idea is to add and subtract two equations, and then solve the unknown by eliminating the terms with the same name. When using the method of addition, subtraction and elimination, it is necessary to make the coefficient of each unknown equal or the inverse equal, and then add and subtract.

Step 2: Solve the problem

The coefficient of each unknown in the equation is equal or the opposite number is equal. Add or subtract these equations to eliminate one unknown and express it as an algebraic expression of another unknown. Solve another unknown, bring the solved unknown into the original equations, and solve other unknowns.

3. Preventive measures

In the process of elimination, there may be indefinite equations or contradictory equations, so it is necessary to choose the most suitable elimination method according to the conditions of the equations. After adding and subtracting multiple equations, it is necessary to check whether all the unknown coefficients are equal or whether the opposites are equal.

4. Application area

Addition, subtraction and elimination are widely used in solving various equations in high school mathematics, and have important applications in mathematical science, physics, chemistry and other fields. It is not only a basic tool method, but also a good way to cultivate students' logical thinking and ability to solve practical problems.

In addition, there are some details and extended knowledge to pay attention to.

5. Exclusion method

In the process of elimination, there are two methods: moving all the unknowns of one equation to another equation, or adding or subtracting the terms with the same name of two equations to eliminate the element. This requires selecting the most appropriate method according to the actual situation of the equations.

6. Indefinite equations and contradictory equations

Some equations can't solve any unknown value through addition, subtraction and elimination, and there may be two situations: indefinite equation and contradictory equation. Indefinite equation means that the system of equations has infinitely many solutions, and contradictory equation means that the system of equations has no solutions. In this case, we need to reconstruct the equation or consider other methods to solve the problem.

7. Common applications

Addition, subtraction and elimination are also widely used in engineering, physics, computer science and other fields. For example, in physics, when solving Newton's law, it is usually necessary to solve multiple equations at the same time to solve multiple unknowns; In computer science, solving linear equations is also one of the important applications of addition, subtraction and elimination.

To sum up, understanding the basic concepts, solving steps and matters needing attention of addition and subtraction will help us to choose and use this method to solve problems more accurately in practical application. In addition, the application of addition, subtraction and elimination method can also be extended to other disciplines, which has broad application prospects.