Question

19．解方程组：$\left\{\begin{array}{l}{\frac{10}{x+y}+\frac{3}{x-y}=-5}\\{\frac{15}{x+y}-\frac{2}{x-y}=-1}\end{array}\right.$．

Answer 1

分析 方程组利用换元法变形后，求出解即可．

解答 解：设$\frac{1}{x+y}$=a，$\frac{1}{x-y}$=b，
方程组变形得：$\left\{\begin{array}{l}{10a+3b=-5}\\{15a-2b=-1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=-\frac{1}{5}}\\{b=-1}\end{array}\right.$，
代入得：$\left\{\begin{array}{l}{x+y=-5}\\{x-y=-1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=-3}\\{y=-2}\end{array}\right.$，
经检验$\left\{\begin{array}{l}{x=-3}\\{y=-2}\end{array}\right.$是原方程组的解．

点评 此题考查了解二元一次方程，利用了换元的思想，熟练掌握运算法则是解本题的关键．