Mastering Linear Equations for Cambridge KS3 Mathematics | 掌握剑桥 KS3 数学中的线性方程

📚 Mastering Linear Equations for Cambridge KS3 Mathematics | 掌握剑桥 KS3 数学中的线性方程

Linear equations are one of the most important building blocks in the Cambridge KS3 mathematics curriculum. They appear in nearly every topic, from solving word problems to understanding graphs and formulas. If you can solve a linear equation confidently, you already have a powerful tool for later work in algebra, geometry and even science. This article takes you through the key ideas step by step, with clear explanations, worked examples and helpful practice tips. It is designed to support classroom learning and revision for tasks such as the exercise on page 183, question 2.

线性方程是剑桥 KS3 数学课程中最重要的基础模块之一。它们几乎出现在每个主题中，从解文字题到理解图像和公式都离不开它。如果你能自信地解出一个线性方程，就已经掌握了代数、几何甚至科学后续学习的强大工具。本文将带你一步步梳理核心概念，提供清晰的解释、例题和实用的练习建议，旨在帮助你巩固课堂所学并复习类似第 183 页第 2 题这样的练习。

1. What is a Linear Equation? | 什么是线性方程？

A linear equation is an equation in which the highest power of the variable is 1. This means the variable, often written as x, is not squared, cubed or raised to any higher power. The general form of a linear equation in one variable can be written as ax + b = c, where a, b and c are numbers and a is not zero.

线性方程是指未知数的最高次数为 1 的方程。这意味着未知数（通常写作 x）不会被平方、立方或进行更高次运算。一元一次方程的一般形式可以写成 ax + b = c，其中 a、b、c 是数字，且 a 不等于 0。

For example, 3x + 5 = 17 and 2(x – 4) = 10 are linear equations. The word ‘linear’ suggests a straight line: when these equations are plotted on a graph, they produce a straight line. Understanding this link between algebra and graphs will help you later with coordinate geometry.

例如，3x + 5 = 17 和 2(x – 4) = 10 都是线性方程。“线性”一词意味着直线：当这些方程在坐标图上绘制时，它们会形成一条直线。理解代数与图像之间的这种联系，将有助于你后续学习坐标几何。

2. The Balancing Method | 平衡法

Think of an equation as a set of balance scales. The left-hand side and the right-hand side must always have the same value. Whatever you do to one side of the equation, you must do exactly the same to the other side. This is the golden rule of solving equations.

把方程想象成一台天平。左边和右边的值必须始终相等。你对方程的一边做了什么，就必须对另一边也做完全相同的操作。这是解方程的金科玉律。

• Add the same number to both sides. 两边同时加上同一个数。
• Subtract the same number from both sides. 两边同时减去同一个数。
• Multiply both sides by the same non-zero number. 两边同时乘以同一个不为 0 的数。
• Divide both sides by the same non-zero number. 两边同时除以同一个不为 0 的数。

This method keeps the equation balanced and helps you isolate the variable step by step.

这种方法能保持方程平衡，帮助你逐步分离出未知数。

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