Question

15．若$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$都是方程ax-by=4的解，求代数式（b-a）²⁰¹²的值．

Answer 1

分析 根据题意直接将$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$代入方程ax-by=4，求出a，b的值进而得出答案．

解答 解：∵$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$都是方程ax-by=4的解，
∴$\left\{\begin{array}{l}{a+2b=4}\\{2a=4}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$，
∴（b-a）²⁰¹²=1．

点评 此题主要考查了二元一次方程组的解法，得出关于a，b的方程组是解题关键．