Question

1．方程组$\left\{\begin{array}{l}{\frac{xy}{3x-2y}=\frac{1}{8}}\\{\frac{xy}{2x+3y}=\frac{1}{7}}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=\frac{13}{5}}\\{y=\frac{13}{38}}\end{array}\right.$．

Answer 1

分析 方程组整理后，利用加减消元法求出x与y的值即可．

解答 解：方程组整理得：$\left\{\begin{array}{l}{8xy=3x-2y①}\\{7xy=2x+3y②}\end{array}\right.$，
①×3+②×2得：38xy=13x，即y=$\frac{13}{38}$，
把y=$\frac{13}{38}$代入①得：x=$\frac{13}{5}$，
则方程组的解为$\left\{\begin{array}{l}{x=\frac{13}{5}}\\{y=\frac{13}{38}}\end{array}\right.$．
故答案为：$\left\{\begin{array}{l}{x=\frac{13}{5}}\\{y=\frac{13}{38}}\end{array}\right.$

点评 此题考查了解二元一次方程组，熟练掌握运算法则是解本题的关键．