题目内容
6．已知方程组$\left\{\begin{array}{l}{4x+y=5}\\{3x-2y=1}\end{array}\right.$和$\left\{\begin{array}{l}{ax+by=3}\\{ax-by=1}\end{array}\right.$有相同的解，求a和b的值．分析 先解方程组$\left\{\begin{array}{l}{4x+y=5}\\{3x-2y=1}\end{array}\right.$求出x，y的值，代入方程组$\left\{\begin{array}{l}{ax+by=3}\\{ax-by=1}\end{array}\right.$，即可解答．
解答 解：方程组$\left\{\begin{array}{l}{4x+y=5}\\{3x-2y=1}\end{array}\right.$得：$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$代入$\left\{\begin{array}{l}{ax+by=3}\\{ax-by=1}\end{array}\right.$得：$\left\{\begin{array}{l}{a+b=3}\\{a-b=1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$．
点评 本题考查了二元一次方程组的解，解决本题的关键是解二元一次方程组．
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