# 方程组

## 解聯立方程式的方法

### 畫圖法

${\displaystyle {\begin{cases}2x+y=8\\x+y=6\end{cases}}}$

 綠色為 ${\displaystyle 2x+y=8\,}$ ，紅色為 ${\displaystyle x+y=6\,}$ 。

${\displaystyle (x,y)=(2,4)}$

${\displaystyle {\begin{cases}x=2\\y=4\end{cases}}}$

### 代入消去法

${\displaystyle {\begin{cases}2x+y=8\\x+y=6\end{cases}}}$

 {\displaystyle {\begin{aligned}2x+y&=8\\y&=8-2x\end{aligned}}} {\displaystyle {\begin{aligned}x+y&=6\\6-x&=y\end{aligned}}} {\displaystyle {\begin{aligned}\backslash \quad &\quad \quad \ /\\8-2x&=6-x\\8-6&=2x-x\\x&=2\end{aligned}}}

{\displaystyle {\begin{aligned}y&=6-x\\&=6-(2)\\&=4\end{aligned}}}

${\displaystyle {\begin{cases}x=2\\y=4\end{cases}}}$

### 加減消去法

${\displaystyle {\begin{cases}2x+y=8\\x+y=6\end{cases}}}$

{\displaystyle {\begin{aligned}\ 2x+y=8\\{\underline {-)\ x+y=6}}\\({\text{subtract}})\ x=2\end{aligned}}}

{\displaystyle {\begin{aligned}x+y&=6&({\text{the second equation}})\\(2)+y&=6\\y&=6-2\\y&=4\end{aligned}}}

${\displaystyle {\begin{cases}x=2\\y=4\end{cases}}}$