Question

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

Answer 1

分析 先設x+3y=m，x-3y=n，再因式分解后進行解答即可．

解答 解：設x+3y=m，x-3y=n，可得$\left\{\begin{array}{l}{{x}^{2}-9{y}^{2}=15}\\{x+3y=5}\end{array}\right.$變形為$\left\{\begin{array}{l}{mn=15}\\{m=5}\end{array}\right.$，
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：$\left\{\begin{array}{l}{x=4}\\{y=\frac{1}{3}}\end{array}\right.$．

點評 此題考查高次方程的解法，熟知解二元一次方程組的加減消元法和代入消元法是解答此題的關(guān)鍵．