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algebra · worked example

Solve 方程組：x+y=10 且 x-y=4

Method: 加減消元法. Verified step-by-step solution with our free AI math solver.
Problem

{x+y=10x−y=4\begin{cases} x + y = 10 \\ x - y = 4 \end{cases}

Step-by-step solution

  1. 將兩個方程式相加以消去 yy：(x+y)+(x−y)=10+4(x+y) + (x-y) = 10 + 4，得到 2x=142x = 14。

  2. 求解：x=7x = 7。

  3. 回代到第一個方程式：7+y=107 + y = 10，因此 y=3y = 3。

  4. 驗證：7−3=47 - 3 = 4 ✓。

Answer

(x,y)=(7,3)(x, y) = (7, 3)

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