Question

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

Answer 1

分析 方程组利用加减消元法求出解即可．

解答 解：$\left\{\begin{array}{l}{\sqrt{2}x+\sqrt{3}y=3\sqrt{2}①}\\{\sqrt{3}x-\sqrt{2}y=2\sqrt{3}②}\end{array}\right.$，
①×$\sqrt{2}$+②×$\sqrt{3}$得：5x=12，即x=$\frac{12}{5}$，
把x=$\frac{12}{5}$代入①得：y=$\frac{\sqrt{6}}{5}$，
则方程组的解为$\left\{\begin{array}{l}{x=\frac{12}{5}}\\{y=\frac{\sqrt{6}}{5}}\end{array}\right.$．

点评 此题考查了解二元一次方程组，利用了消元的思想，消元的方法有：代入消元法与加减消元法．