Question

2．如果$\left\{\begin{array}{l}x=a\\ y=b\end{array}\right.$是二元一次方程組$\left\{\begin{array}{l}x-y=1\\ x+y=-3\end{array}\right.$的解，那么a²-b²的值為（　　）

• A． 5
• B． 3
• C． 1
• D． -3

Answer 1

分析 將$\left\{\begin{array}{l}x=a\\ y=b\end{array}\right.$代入二元一次方程組$\left\{\begin{array}{l}x-y=1\\ x+y=-3\end{array}\right.$，求出a，b的值，即可解答．

解答 解：將$\left\{\begin{array}{l}x=a\\ y=b\end{array}\right.$代入二元一次方程組$\left\{\begin{array}{l}x-y=1\\ x+y=-3\end{array}\right.$，得：
$\left\{\begin{array}{l}{a-b=1}\\{a+b=-3}\end{array}\right.$
解得：$\left\{\begin{array}{l}{a=-1}\\{b=-2}\end{array}\right.$
∴a²-b²=（-1）²-（-2）²=1-4=-3．
故選：D．

點評 本題考查了二元一次方程組的解，解決本題的關鍵是解二元一次方程組．