📚 Simultaneous Equations in IGCSE Mathematics | IGCSE 数学联立方程精讲
In IGCSE Mathematics, simultaneous equations appear frequently in both Core and Extended papers. They require you to find values of unknowns that satisfy two or more equations at the same time. This article explains elimination, substitution, graphical methods, word problems, and common errors.
在 IGCSE 数学中，联立方程在 Core 和 Extended 试卷中都经常出现。它要求你求出同时满足两个或更多方程的未知数的值。本文将讲解消元法、代入法、图像法、应用题和常见错误。
1. What Are Simultaneous Equations? | 什么是联立方程？
A simultaneous equation system contains two or more variables and an equal number of independent equations. For example, 2x + y = 7 and x – y = 2 form a system with two unknowns. A solution is an ordered pair (x, y) that makes both equations true at the same time.
联立方程组包含两个或更多变量以及相同数量的独立方程。例如，2x + y = 7 和 x – y = 2 组成一个含有两个未知数的方程组。解是同时使两个方程都成立的有序数对 (x, y)。
If there are two unknowns, you generally need two equations. One equation alone has infinitely many solutions.
如果有两个未知数，通常需要两个方程。单独一个方程有无穷多个解。
2x + y = 7, x – y = 2 → x = 3, y = 1
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