📚 IGCSE Maths: Solving Simultaneous Equations | IGCSE 数学：解联立方程
Simultaneous equations appear throughout the IGCSE Mathematics syllabus, from basic linear pairs to extended problems involving one quadratic equation. They test your ability to find values that satisfy two or more conditions at the same time.
联立方程在 IGCSE 数学大纲中贯穿始终，从基础的二元一次方程组，到拓展卷中涉及一条二次方程的问题。它考查你是否能求出同时满足两个或更多条件的未知数值。
1. What Are Simultaneous Equations? | 什么是联立方程？
A simultaneous equation system asks you to find the unknowns that satisfy all given equations at once. In IGCSE, most systems have two equations and two unknowns, usually written as x and y.
联立方程组要求你求出同时满足所有给定方程的未知数。在 IGCSE 中，大多数方程组含有两个方程和两个未知数，通常写作 x 和 y。
For example, the pair x + y = 7 and x − y = 1 has the single solution x = 4, y = 3 because these values make both equations true.
例如，方程组 x + y = 7 和 x − y = 1 的唯一解是 x = 4，y = 3，因为这两个值同时使两个方程成立。
You should always check a solution by substituting the values back into both original equations.
你应当始终把解代回两个原方程进行检验。
2. The Graphical Idea | 图像意义
Each linear equation in two variables represents a straight line on the coordinate plane. The solution to a pair of simultaneous equations is the point where the two lines cross.
每个二元一次方程在坐标平面上表示一条直线。二元一次方程组的解就是两条直线相交的点。
s geometric view helps explain why some systems have no solution or infinitely many solutions.
对于上面的方程，直线 x + y = 7 与 x − y = 1 相交于点 (4, 3)。这种几何观点有助于解释为什么有些方程组无解或有无穷多解。
In the IGCSE core course, you are often asked to solve equations algebraically, but a sketch can help you check whether your answer is reasonable.
在 IGCSE 核心课程中，你常常被要求用代数方法解方程，但画一个草图可以帮助你检查答案是否合理。
3. Solving by Elimination | 消元法
ons are in the form ax + by = c. You add or subtract the equations to remove one variable.
当两个方程都形如 ax + by = c 时，消元法通常是最快的方法。你将两个方程相加或相减，以消去一个未知数。
Worked example:
例题：
2x + y = 10
x − y = 2
so 3x = 12, giving x = 4. Then substitute x = 4 into x − y = 2 to get 4 − y = 2, so y = 2.
将两个方程相加：(2x + y) + (x − y) = 10 + 2，得到 3x = 12，所以 x = 4。然后把 x = 4 代入 x − y = 2，得 4 − y = 2，所以 y = 2。
If the coefficients of one variable are not equal, multiply one or both equations first so that the coefficients match.
如果某个未知数的系数不相等，先将一个或两个方程乘以适当的数，使系数相同。
For example, to solve 3x + 2y = 12 and 5x − 2y = 4 nts are already +2 and −2, so adding the equations immediately gives 8x = 16, hence x = 2.
例如，要解 3x + 2y = 12 和 5x −
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com 更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图