Solving Simultaneous Equations | 解联立方程

📚 Solving Simultaneous Equations | 解联立方程

Simultaneous equations are a pair (or more) of equations that share two unknown variables. To solve them, you must find values of the unknowns that satisfy every equation at the same time. This is one of the most important skills in IGCSE Mathematics, and it appears in both Paper 2 and Paper 4 across many different question formats.

联立方程是指两个（或以上）共享两个未知数的方程。解联立方程就是找到一组未知数的值，使每一个方程同时成立。这是 IGCSE 数学中最重要的技能之一，在 Paper 2 和 Paper 4 中都会以多种题型出现。

1. The Basics of Simultaneous Equations | 联立方程基础

A linear equation in two unknowns has the general form ax + by = c, where a, b and c are constants. For example, 2x + y = 7 is a linear equation in x and y. A single linear equation with two variables has infinitely many solutions; you need a second independent equation to find a unique solution pair (x, y).

含有两个未知数的线性方程一般形式为 ax + by = c，其中 a、b、c 是常数。例如，2x + y = 7 就是关于 x 和 y 的线性方程。单独一个含两个变量的线性方程有无数个解；你需要第二个独立的方程才能求出唯一的一组解 (x, y)。

Geometrically, the solutions of a linear equation in two variables form a straight line in the coordinate plane. When you have two equations, their graphs are two lines; the intersection point of these lines gives the simultaneous solution. This visual understanding will help you later when you study coordinate geometry and straight-line graphs.

从几何角度看，一个含两个变量的线性方程的解在坐标平面上形成一条直线。当你拥有两个方程时，它们的图像就是两条直线；两条直线的交点就是联立方程组的解。这种直观理解会在你后续学习坐标几何

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