simultaneous equations

简明释义

联立方程

英英释义

例句

1.The method of substitution can be used to solve simultaneous equations 联立方程 effectively.

替代法可以有效地用于解决 simultaneous equations 联立方程。

2.To find the intersection point of two lines, we need to solve their simultaneous equations 联立方程.

要找到两条线的交点，我们需要解它们的 simultaneous equations 联立方程。

3.In algebra, we often solve simultaneous equations 联立方程 to find the values of multiple variables.

在代数中，我们经常解 simultaneous equations 联立方程 来找到多个变量的值。

4.In engineering, simultaneous equations 联立方程 are often used to model systems with multiple interacting components.

在工程中，simultaneous equations 联立方程 常用于建模具有多个相互作用组件的系统。

5.The teacher demonstrated how to graph simultaneous equations 联立方程 on the coordinate plane.

老师演示了如何在坐标平面上绘制 simultaneous equations 联立方程。

作文

In the realm of mathematics, the study of equations is fundamental to understanding various concepts and solving real-world problems. Among the different types of equations, simultaneous equations are particularly significant. These are sets of equations with multiple variables that are solved together, meaning that they share common solutions. The importance of simultaneous equations lies in their ability to model situations where multiple conditions must be satisfied at the same time.Consider a simple example involving two variables, x and y. If we have two equations: 2x + 3y = 6 and x - y = 2, we can solve these equations simultaneously to find the values of x and y that satisfy both equations. This process can be achieved through various methods, such as substitution, elimination, or graphical representation. Each method offers unique advantages depending on the complexity of the equations involved.The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation. For instance, from the second equation, we can express x as x = y + 2. Substituting this into the first equation gives us a single equation in terms of y, which can then be solved easily. Once we find y, we can substitute back to find x.On the other hand, the elimination method focuses on eliminating one variable by combining the equations. This can often be more straightforward, especially when the coefficients of one variable can be made equal. By adding or subtracting the equations, we can isolate one variable and solve for it directly.Graphically, simultaneous equations represent lines on a coordinate plane. The point where the lines intersect is the solution to the equations, indicating the values of x and y that satisfy both conditions. This visual representation not only aids in understanding the concept but also provides insight into the nature of the solutions—whether they are unique, infinite, or nonexistent.The application of simultaneous equations extends far beyond mere academic exercises. They are essential in fields such as engineering, economics, and physics, where multiple factors interact simultaneously. For example, engineers might use simultaneous equations to determine the forces acting on a structure, ensuring stability and safety. In economics, they can model supply and demand scenarios, helping businesses make informed decisions.Moreover, the ability to solve simultaneous equations equips individuals with critical thinking and problem-solving skills. It encourages logical reasoning and the ability to analyze complex situations by breaking them down into manageable parts. These skills are invaluable in both professional and personal contexts, as they foster a systematic approach to tackling challenges.In conclusion, simultaneous equations are a vital component of mathematics that allows us to solve problems involving multiple variables. Their applications are widespread, impacting various fields and enhancing our analytical abilities. Understanding how to work with simultaneous equations not only enriches our mathematical knowledge but also prepares us for real-world situations where multiple conditions must be satisfied simultaneously. As we continue to encounter complex problems in our daily lives, the skills gained from mastering simultaneous equations will undoubtedly prove beneficial.

在数学领域，方程的研究对于理解各种概念和解决现实问题至关重要。在不同类型的方程中，simultaneous equations（联立方程）尤其重要。这些是具有多个变量的方程组，它们一起被求解，这意味着它们共享共同的解。simultaneous equations的重要性在于它们能够建模多种条件必须同时满足的情况。考虑一个涉及两个变量x和y的简单例子。如果我们有两个方程：2x + 3y = 6和x - y = 2，我们可以同时求解这些方程，以找到满足两个方程的x和y的值。这个过程可以通过多种方法实现，例如代入法、消元法或图形表示。每种方法根据所涉及方程的复杂性提供独特的优势。代入法涉及将其中一个方程解出一个变量，然后将该表达式代入另一个方程。例如，从第二个方程中，我们可以将x表示为x = y + 2。将其代入第一个方程会给我们一个关于y的单一方程，可以很容易地求解。一旦找到y，我们可以再代入回去找到x。另一方面，消元法则侧重于通过组合方程消去一个变量。这通常更直接，特别是当一个变量的系数可以相等时。通过加法或减法，我们可以直接隔离一个变量并求解它。在图形上，simultaneous equations在坐标平面上表示直线。直线交点即为方程的解，表示满足两个条件的x和y的值。这种可视化表示不仅有助于理解概念，还提供了对解的性质的洞察——无论它们是唯一的、无限的还是不存在的。simultaneous equations的应用远不止学术练习。它们在工程、经济学和物理等领域中至关重要，在这些领域中，多个因素同时相互作用。例如，工程师可能会使用simultaneous equations来确定作用在结构上的力，以确保稳定性和安全性。在经济学中，它们可以建模供需场景，帮助企业做出明智的决策。此外，解决simultaneous equations的能力使个人具备批判性思维和解决问题的技能。它鼓励逻辑推理和通过将复杂情况分解为可管理部分来分析的能力。这些技能在专业和个人背景中都是无价的，因为它们促进了系统化的方法来应对挑战。总之，simultaneous equations是数学中一个重要的组成部分，使我们能够解决涉及多个变量的问题。它们的应用广泛，影响着各个领域，并增强我们的分析能力。理解如何处理simultaneous equations不仅丰富了我们的数学知识，还为我们准备了面对现实世界中必须同时满足多个条件的复杂问题。当我们在日常生活中继续遇到复杂问题时，掌握simultaneous equations所获得的技能无疑将证明是有益的。