📚 IGCSE Mathematics: Linear Equations, Simultaneous Equations and Inequalities | IGCSE 数学：线性方程、联立方程与不等式
Linear equations, simultaneous equations and inequalities form a central part of the IGCSE Mathematics algebra syllabus. These topics appear in both Core and Extended papers, often as structured questions in Paper 2 and Paper 4. Mastering the basic techniques of balancing equations, eliminating variables and reversing inequality signs under negative multiplication will give you a strong foundation for harder topics such as quadratic functions, linear programming and coordinate geometry.
线性方程、联立方程和不等式是 IGCSE 数学代数部分的核心内容。这些主题在核心和扩展试卷中都会出现，通常以结构化题目的形式出现在 Paper 2 和 Paper 4 中。掌握方程两边平衡、消元以及不等式乘除负数时改变不等号方向等基本技巧，将为你学习二次函数、线性规划和坐标几何等更难的专题打下坚实基础。
1. What Are Linear Equations? | 什么是线性方程？
A linear equation is an equation in which the highest power of the unknown variable is 1. For example, 2x + 5 = 17 is linear because x appears to the power 1. The general form is ax + b = c, where a, b and c are constants and a ≠ 0.
线性方程是指未知数的最高次数为 1 的方程。例如 2x + 5 = 17 就是线性方程，因为 x 的指数为 1。一般形式为 ax + b = c，其中 a、b、c 为常数，且 a ≠ 0。
The solution of a linear equation is the value of the variable that makes both sides equal. You can check your solution by substituting it back into the original equation.
线性方程的解就是使等号两边相等的变量值。你可以将解代回原方程来检验答案。
2. Solving One-Step and Two-Step Equations | 解一步与两步方程
To solve an equation, you must keep the equation balanced by performing the same operation on both sides. For a one-step equation such as x + 7 = 12, subtract 7 from both sides to obtain x = 5.
解方程时，你必须对等号两边同时进行相同的运算以保持平衡。对于一步方程，如 x + 7 = 12，两边同时减去 7，得到 x = 5。
For a two-step equation such as 2x + 5 = 17, first subtract 5 from both sides, then divide both sides by 2:
对于两步方程，如 2x + 5 = 17，先两边同时减 5，再两边同时除以 2：
2x + 5 − 5 = 17 − 5 → 2x = 12 → x = 6
Always use inverse operations: addition undoes subtraction, multiplication undoes division, and vice versa.
请始终使用逆运算：加法抵消减法，乘法抵消除法，反之亦然。
3. Equations with Brackets and
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