1, determine the unknown: First, we need to determine the unknown in the problem. Unknown numbers are usually represented by letters, such as x, y, z, etc. Build relationships: Next, we need to build relationships between unknowns based on the information in the question. These relationships can be equal, unequal or proportional.
2. Collating relationships: Collating established relationships to make them conform to the form of equations. If there is a constant term in the relationship, it needs to be moved to the other side of the equation. Solving the equation: Finally, solve the equation by algebraic operation to get the unknown value. This can be achieved by substitution, elimination and collocation.
3. It should be noted that when listing equations, it is necessary to ensure that the established relationship is consistent with the information in the problem, and the solution of the equation should be unique and meaningful. In addition, we need to pay attention to the consistency of symbols and units in the equation. The column equation method can be applied to various mathematical problems, including algebraic equations, geometric equations and trigonometric equations.
Matters needing attention in column equation
1, column equation is a common method to solve mathematical problems, but in practical application, we need to pay attention to the following points: determine the unknown quantity: before column equation, we need to make clear the unknown quantity in the problem and express it with letters or symbols. The selection of unknowns should be as simple and clear as possible, which is convenient for subsequent calculation and derivation.
2. Establish relational expression: according to the information in the question, establish the relationship between the unknowns. These relationships can be equal, unequal or proportional. When establishing a relationship, we should pay attention to the accuracy of logical reasoning and mathematical operation. Collating relationships: collating established relationships to make them conform to the form of equations.
3. If there is a constant term in the relationship, you need to move it to the other side of the equation. At the same time, we should pay attention to the consistency of symbols and units in the equation. Solving the equation: through algebraic operation, the unknown value can be obtained by solving the equation. This can be achieved by substitution, elimination and collocation. Pay attention to the order and accuracy of operation when solving equations to avoid mistakes.
4. Check the rationality of the solution: after getting the solution of the equation, you need to check whether the solution meets the requirements and conditions of the problem. By substituting the solution into the original equation or relationship, it can be verified whether the equation or other conditions are met. Pay attention to special situations: In practical problems, there may be some special situations, such as no solution, multiple solutions or infinite solutions.