simultaneous equations

简明释义

联立方程

英英释义

例句

1.In chemistry, simultaneous equations 联立方程 can be used to balance chemical reactions.

在化学中，simultaneous equations 联立方程可以用来平衡化学反应。

2.To find the intersection of two lines, we can solve the simultaneous equations 联立方程 that represent them.

为了找到两条直线的交点，我们可以解这两个代表它们的simultaneous equations 联立方程。

3.Solving simultaneous equations 联立方程 is essential for finding the values of variables in a complex system.

解simultaneous equations 联立方程对于在复杂系统中找到变量的值至关重要。

4.In economics, we often use simultaneous equations 联立方程 to model supply and demand.

在经济学中，我们经常使用simultaneous equations 联立方程来建模供需关系。

5.The engineer applied simultaneous equations 联立方程 to determine the forces acting on the structure.

工程师应用simultaneous equations 联立方程来确定作用于结构上的力。

作文

Simultaneous equations are a fundamental concept in algebra that involves solving multiple equations at the same time. These equations typically contain two or more variables, and the goal is to find the values of these variables that satisfy all the equations simultaneously. This concept is crucial not only in mathematics but also in various fields such as physics, engineering, economics, and computer science. Understanding simultaneous equations (联立方程) allows students to tackle complex problems where multiple conditions must be met.To illustrate this, consider a simple example involving two equations: the first equation could represent the cost of apples and oranges, while the second might represent the total number of fruits purchased. By setting up the equations, we can find out how many apples and oranges were bought without needing additional information. This practical application of simultaneous equations (联立方程) showcases their relevance in everyday scenarios.Solving simultaneous equations (联立方程) can be approached in several ways, including graphing, substitution, and elimination methods. The graphing method involves plotting each equation on a coordinate plane and identifying the point where they intersect, which represents the solution. However, this method may not always be feasible for complex equations or when dealing with a large number of variables.The substitution method is another effective technique where one equation is solved for one variable, and this expression is substituted into the other equation. For instance, if we have the equations x + y = 10 and 2x - y = 3, we can solve the first equation for y, giving us y = 10 - x. We then substitute this into the second equation to find the value of x. Once we have x, we can easily find y. This method highlights the interconnectedness of simultaneous equations (联立方程) as each equation feeds into the other.Elimination is yet another method to solve simultaneous equations (联立方程). In this technique, we aim to eliminate one variable by adding or subtracting the equations. For example, if we have the same two equations, we can multiply the first equation by 2 to align the coefficients of x, allowing us to eliminate x when we subtract the second equation from it. This method often leads to quicker solutions, especially when dealing with larger systems of equations.In real-world applications, simultaneous equations (联立方程) are used extensively. For instance, engineers use them to design structures, economists apply them to model market behavior, and scientists employ them to analyze data. The ability to solve these equations is essential for making informed decisions based on multiple criteria.Moreover, mastering simultaneous equations (联立方程) is a stepping stone to more advanced mathematical concepts, such as linear programming and matrix algebra. As students progress in their studies, they will encounter increasingly complex systems of equations, reinforcing the importance of a solid foundation in this area.In conclusion, simultaneous equations (联立方程) play a vital role in both academic and practical contexts. Whether through graphing, substitution, or elimination, the ability to solve these equations equips individuals with essential problem-solving skills. As we continue to encounter challenges that require simultaneous solutions, the knowledge of simultaneous equations (联立方程) will remain invaluable in our ever-evolving world.

联立方程是代数中的一个基本概念，涉及同时求解多个方程。这些方程通常包含两个或更多变量，目标是找到满足所有方程的变量值。这个概念不仅在数学中至关重要，还在物理、工程、经济学和计算机科学等多个领域中发挥着重要作用。理解simultaneous equations（联立方程）使学生能够解决复杂问题，在这些问题中必须满足多个条件。为了说明这一点，考虑一个简单的例子，涉及两个方程：第一个方程可以表示苹果和橙子的成本，而第二个方程可能表示购买的水果总数。通过设置方程，我们可以找出购买了多少苹果和橙子，而不需要额外的信息。这个实际应用展示了simultaneous equations（联立方程）的相关性，尤其是在日常场景中。解决simultaneous equations（联立方程）可以通过几种方法进行，包括图形法、代入法和消元法。图形法涉及在坐标平面上绘制每个方程，并识别它们交叉的点，这个点代表了解决方案。然而，对于复杂方程或处理大量变量时，这种方法可能并不总是可行。代入法是另一种有效的技术，其中一个方程被解出一个变量，然后将这个表达式代入另一个方程。例如，如果我们有方程x + y = 10和2x - y = 3，我们可以解出第一个方程中的y，得到y = 10 - x。然后我们将这个结果代入第二个方程以找到x的值。一旦我们得到了x，就可以轻松找到y。这个方法突显了simultaneous equations（联立方程）的相互关联性，因为每个方程都影响着另一个方程。消元法是解决simultaneous equations（联立方程）的另一种方法。在这种技术中，我们旨在通过加法或减法消去一个变量。例如，如果我们有相同的两个方程，我们可以将第一个方程乘以2，以对齐x的系数，从而在减去第二个方程时消去x。这种方法通常会导致更快的解决方案，特别是在处理较大的方程组时。在现实世界的应用中，simultaneous equations（联立方程）被广泛使用。例如，工程师使用它们来设计结构，经济学家应用它们来建模市场行为，科学家利用它们来分析数据。解决这些方程的能力对于根据多个标准做出明智的决策至关重要。此外，掌握simultaneous equations（联立方程）是更高级数学概念的基础，例如线性规划和矩阵代数。随着学生在学习上的进步，他们将遇到越来越复杂的方程组，进一步巩固了这一领域扎实基础的重要性。总之，simultaneous equations（联立方程）在学术和实际环境中发挥着重要作用。无论是通过图形法、代入法还是消元法，解决这些方程的能力为个人提供了必要的问题解决技能。随着我们继续面临需要同时解决的挑战，了解simultaneous equations（联立方程）在我们不断发展的世界中将保持无价。