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algebra · worked example

Solve 聯立方程式：3x+2y=12 與 x-y=1

Method: 代入法. Verified step-by-step solution with our free AI math solver.
Problem

{3x+2y=12x−y=1\begin{cases} 3x + 2y = 12 \\ x - y = 1 \end{cases}

Step-by-step solution

  1. 由第二個方程式解出 xx：x=y+1x = y + 1。

  2. 代入第一個方程式：3(y+1)+2y=123(y + 1) + 2y = 12。

  3. 展開：3y+3+2y=123y + 3 + 2y = 12，所以 5y=95y = 9。

  4. 求解：y=95y = \tfrac{9}{5}。

  5. 回代：x=95+1=145x = \tfrac{9}{5} + 1 = \tfrac{14}{5}。

Answer

(x,y)=(145, 95)(x, y) = \bigl(\tfrac{14}{5},\ \tfrac{9}{5}\bigr)

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