Question

2．已知关于x，y的方程组$\left\{\begin{array}{l}{ax+by=7.5}\\{ax-by=10}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=-1}\\{y=-2}\end{array}\right.$，则关于x₁，y₁的方程组$\left\{\begin{array}{l}{a（{x}_{1}+1）+b（{y}_{1}-1）=7.5}\\{a（{x}_{1}+1）-b（{y}_{1}-1）=10}\end{array}\right.$的解是$\left\{\begin{array}{l}{{x}_{1}=-2}\\{{y}_{1}=-1}\end{array}\right.$．

Answer 1

分析 仿照已知方程组的解法，求出所求方程组的解即可．

解答 解：根据题意得：$\left\{\begin{array}{l}{{x}_{1}+1=-1}\\{{y}_{1}-1=-2}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{{x}_{1}=-2}\\{{y}_{1}=-1}\end{array}\right.$，
则关于x₁，y₁的方程组$\left\{\begin{array}{l}{a（{x}_{1}+1）+b（{y}_{1}-1）=7.5}\\{a（{x}_{1}+1）-b（{y}_{1}-1）=10}\end{array}\right.$的解是$\left\{\begin{array}{l}{{x}_{1}=-2}\\{{y}_{1}=-1}\end{array}\right.$．
故答案为：$\left\{\begin{array}{l}{{x}_{1}=-2}\\{{y}_{1}=-1}\end{array}\right.$

点评 此题考查了解二元一次方程组，利用了消元的思想，消元的方法有：代入消元法与加减消元法．