Question

5．方程组$\left\{\begin{array}{l}{\frac{1}{x}+\frac{1}{y}=5}\\{xy=\frac{1}{6}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=\frac{1}{2}}\\{y=\frac{1}{3}}\end{array}\right.$或$\left\{\begin{array}{l}{x=\frac{1}{3}}\\{y=\frac{1}{2}}\end{array}\right.$．

Answer 1

分析 化简方程组可得$\left\{\begin{array}{l}{x+y=\frac{5}{6}}\\{xy=\frac{1}{6}}\end{array}\right.$，从而解得．

解答 解：∵$\left\{\begin{array}{l}{\frac{1}{x}+\frac{1}{y}=5}\\{xy=\frac{1}{6}}\end{array}\right.$，
∴$\left\{\begin{array}{l}{x+y=\frac{5}{6}}\\{xy=\frac{1}{6}}\end{array}\right.$，
解得，$\left\{\begin{array}{l}{x=\frac{1}{2}}\\{y=\frac{1}{3}}\end{array}\right.$或$\left\{\begin{array}{l}{x=\frac{1}{3}}\\{y=\frac{1}{2}}\end{array}\right.$；
故答案为：$\left\{\begin{array}{l}{x=\frac{1}{2}}\\{y=\frac{1}{3}}\end{array}\right.$或$\left\{\begin{array}{l}{x=\frac{1}{3}}\\{y=\frac{1}{2}}\end{array}\right.$．

点评 本题考查了方程组的求解方法，属于基础题．