Question

20．解方程组：$\left\{\begin{array}{l}{x^2}-9{y^2}=15\\ x+3y=5\end{array}\right.$．

Answer 1

分析 先设x+3y=m，x-3y=n，再因式分解后进行解答即可．

解答 解：设x+3y=m，x-3y=n，可得$\left\{\begin{array}{l}{{x}^{2}-9{y}^{2}=15}\\{x+3y=5}\end{array}\right.$变形为$\left\{\begin{array}{l}{mn=15}\\{m=5}\end{array}\right.$，
解得：m=5，n=3，
所以可得$\left\{\begin{array}{l}{x+3y=5}\\{x-3y=3}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=4}\\{y=\frac{1}{3}}\end{array}\right.$．

点评 此题考查高次方程的解法，熟知解二元一次方程组的加减消元法和代入消元法是解答此题的关键．