Question

11．解方程組：$\left\{\begin{array}{l}{x+2y=6}\\{{x}^{2}-3xy+2{y}^{2}=0}\end{array}\right.$．

Answer 1

分析 由②得出x-2y=0，x-y=0，這樣轉(zhuǎn)化成兩個方程組，求出方程組的解即可．

解答 解：$\left\{\begin{array}{l}{x+2y=6①}\\{{x}^{2}-3xy+2{y}^{2}=0②}\end{array}\right.$
由②得，x-2y=0，x-y=0，
原方程組化為$\left\{\begin{array}{l}{x+2y=6}\\{x-y=0}\end{array}\right.$或$\left\{\begin{array}{l}{x+2y=6}\\{x-2y=0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{{x}_{1}=2}\\{{y}_{1}=2}\end{array}\right.$，$\left\{\begin{array}{l}{{x}_{2}=3}\\{{y}_{2}=\frac{3}{2}}\end{array}\right.$，
∴原方程組的解是 $\left\{\begin{array}{l}{{x}_{1}=2}\\{{y}_{1}=2}\end{array}\right.$，$\left\{\begin{array}{l}{{x}_{2}=3}\\{{y}_{2}=\frac{3}{2}}\end{array}\right.$．

點評 本題考查了解高次方程組，能把方程組轉(zhuǎn)化成二元一次方程組是解此題的關(guān)鍵．