Solving Simultaneous Equations | 联立方程的解法

📚 Solving Simultaneous Equations | 联立方程的解法

Simultaneous equations are a core topic in IGCSE Mathematics. A system of linear simultaneous equations consists of two equations with two unknown variables, and solving it means finding the values of the variables that satisfy both equations at the same time. This skill appears frequently in both Paper 2 and Paper 4, and it is also essential for solving problems in coordinate geometry and other higher-level topics.

联立方程是 IGCSE 数学的核心考点。二元一次联立方程组包含两个含有两个未知数的方程，解联立方程就是找到同时满足这两个方程的未知数的值。这一技能在 Paper 2 和 Paper 4 中频繁出现，同时也是解决坐标几何及其他高阶问题的基础。

1. What Are Simultaneous Equations? | 什么是联立方程？

In IGCSE Mathematics, a linear equation in two variables such as 2x + y = 7 represents a straight line on the coordinate plane. When we have two such equations, we call them simultaneous equations because we seek a common solution that works for both lines at the same time.

在 IGCSE 数学中，形如 2x + y = 7 的二元一次方程在坐标平面上表示一条直线。当我们拥有两个这样的方程时，我们称它们为联立方程，因为我们寻找的是一个能同时满足两条直线的公共解。

The general form of a pair of linear simultaneous equations is:

一般形式的二元一次联立方程为：

a₁x + b₁y = c₁ 且 a₂x + b₂y = c₂

where a₁, a₂, b₁, b₂, c₁, c₂ are constants, and x and y are the unknown variables. A solution is an ordered pair (x, y) that makes both equations true.

其中 a₁、a₂、b₁、b₂、c₁、c₂ 为常数，x 和 y 为未知数。解是一个有序数对 (x, y)，它能使两个方程同时成立。

The solution (x, y) corresponds to the point where the two lines intersect on a graph. There are three main methods taught at IGCSE level: the elimination method, the substitution method, and the graphical method. Each has its own advantages depending on the form of the

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）