Question

18．已知方程組$\left\{\begin{array}{l}{2x+5y=-6①}\\{ax-by=4②}\end{array}\right.$和方程組$\left\{\begin{array}{l}{3x-5y=16①}\\{bx+ay=-8②}\end{array}\right.$的解相同，求代數式（a+2b）²⁰⁰⁹的值．

Answer 1

分析 聯立兩方程組中不含a與b的方程求出解，代入剩下方程求出a與b的值，代入原式計算即可求出值．

解答 解：聯立得：$\left\{\begin{array}{l}{2x+5y=-6}\\{3x-5y=16}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=2}\\{y=-2}\end{array}\right.$，
代入得：$\left\{\begin{array}{l}{a+b=2}\\{a-b=4}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=3}\\{b=-1}\end{array}\right.$，
則原式=1．

點評 此題考查了二元一次方程組的解，方程組的解即為能使方程組中兩方程都成立的未知數的值．