system of equations

简明释义

联立方程

英英释义

例句

1.The engineer used a system of equations 方程组 to determine the forces acting on the structure.

工程师使用system of equations 方程组来确定作用于结构的力。

2.In this math class, we'll learn how to solve a system of equations 方程组 using substitution.

在这节数学课上，我们将学习如何使用代入法解决system of equations 方程组。

3.To solve the problem, we need to set up a system of equations 方程组 that represents the relationships between the variables.

为了解决这个问题，我们需要建立一个表示变量之间关系的system of equations 方程组。

4.A system of equations 方程组 can have one solution, no solution, or infinitely many solutions.

一个system of equations 方程组可以有一个解、没有解或无穷多个解。

5.In economics, a system of equations 方程组 can be used to model supply and demand.

在经济学中，system of equations 方程组可以用来模拟供需关系。

作文

In mathematics, a system of equations is a set of two or more equations with the same variables. Solving a system of equations involves finding the values of the variables that satisfy all the equations simultaneously. This concept is fundamental in various fields, including engineering, physics, economics, and computer science. Understanding how to work with a system of equations can greatly enhance one's problem-solving skills and analytical thinking. To illustrate the importance of a system of equations, let’s consider a real-world application. Suppose you are tasked with determining the intersection point of two lines represented by linear equations. Each line can be expressed as an equation, such as y = 2x + 3 and y = -x + 1. By setting these equations equal to each other, you create a system of equations that can be solved to find the coordinates of their intersection. This is not just an abstract mathematical exercise; it has practical implications in fields like navigation and robotics, where precise calculations are crucial.There are several methods to solve a system of equations. The most common techniques include substitution, elimination, and using matrices. The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. This method is particularly useful when one equation is easily solvable for one variable. On the other hand, the elimination method entails adding or subtracting equations to eliminate a variable, making it easier to solve for the remaining variable. For larger systems, matrix methods, such as Gaussian elimination or using the inverse of a matrix, can be efficient and effective.Moreover, the concept of a system of equations extends beyond linear equations. Nonlinear systems, which may involve quadratic or exponential equations, also fall under this category. Solving nonlinear systems of equations can be more complex and may require numerical methods or graphing techniques to approximate solutions. This complexity highlights the diversity of problems that can be modeled with systems of equations and the necessity for flexible problem-solving strategies.In conclusion, mastering the concept of a system of equations is essential for anyone studying mathematics or related fields. It provides a framework for tackling a wide range of problems and encourages logical reasoning and critical thinking. Whether in academia or professional practice, the ability to analyze and solve systems of equations is a valuable skill that can lead to successful outcomes in various scenarios. As we continue to encounter increasingly complex challenges in our world, the relevance of systems of equations will only grow, making it imperative for learners to engage deeply with this topic and develop their capabilities in this area.

在数学中，方程组是一组具有相同变量的两个或多个方程。解决一个方程组涉及找到同时满足所有方程的变量值。这个概念在工程、物理、经济学和计算机科学等多个领域中是基础性的。理解如何处理方程组可以极大地提高一个人的解决问题能力和分析思维。为了说明方程组的重要性，假设你被要求确定由线性方程表示的两条直线的交点。每条直线可以用一个方程表示，例如y = 2x + 3和y = -x + 1。通过将这些方程设置为相等，你创建了一个可以解决的方程组，以找到它们交点的坐标。这不仅仅是一个抽象的数学练习；它在导航和机器人等领域具有实际意义，在这些领域中，精确的计算至关重要。有几种方法可以解决方程组。最常见的技术包括代入法、消元法和使用矩阵。代入法涉及为一个变量解一个方程，然后将该表达式代入另一个方程中。这种方法在一个方程易于求解一个变量时特别有用。另一方面，消元法则涉及加或减方程以消去一个变量，从而使得更容易求解剩余的变量。对于较大的系统，矩阵方法，如高斯消元法或使用矩阵的逆，可以有效且高效。此外，方程组的概念超出了线性方程的范围。非线性系统，可能涉及二次方程或指数方程，也属于这一类别。解决非线性方程组可能更复杂，可能需要数值方法或图形技术来近似解决方案。这种复杂性突显了可以用方程组建模的问题的多样性，以及灵活的解决问题策略的必要性。总之，掌握方程组的概念对任何学习数学或相关领域的人来说都是至关重要的。它提供了解决各种问题的框架，并鼓励逻辑推理和批判性思维。无论是在学术界还是专业实践中，分析和解决方程组的能力都是一项宝贵的技能，可以在各种场景中取得成功的结果。随着我们继续遇到越来越复杂的挑战，方程组的相关性只会增加，这使得学习者必须深入参与这一主题，并发展他们在这一领域的能力。