Question

13．若$\left\{\begin{array}{l}{x=-3}\\{y=2}\end{array}\right.$是$\left\{\begin{array}{l}{αx+θy=1}\\{θx-βy=-2}\end{array}\right.$的解，则α、β之间的关系是（　　）

• A． β-9α=1
• B． 9α+4β=1
• C． 3α+2β=1
• D． 4β-9α+1=0

Answer 1

分析 把$\left\{\begin{array}{l}{x=-3}\\{y=2}\end{array}\right.$代入$\left\{\begin{array}{l}{αx+θy=1}\\{θx-βy=-2}\end{array}\right.$得关于θ、α、β的方程组，再利用加减消元法消去未知数θ即可．

解答 解：把$\left\{\begin{array}{l}{x=-3}\\{y=2}\end{array}\right.$代入$\left\{\begin{array}{l}{αx+θy=1}\\{θx-βy=-2}\end{array}\right.$得：$\left\{\begin{array}{l}{-3α+2θ=1①}\\{-3θ-2β=-1②}\end{array}\right.$，
①×3+②×2得：-9α-4β=-1③，
③×（-1）得：9α+4β=1，
故选：B．

点评 此题主要考查了二元一次方程组的解，关键是掌握方程组的解同时满足两个方程．