Question

7．已知關(guān)于x、y的二元一次方程組${\left\{\begin{array}{l}{2x+y=3}\\{x-y=3m}\end{array}\right.}\\{\;}\end{array}\right.$的解x、y的值互為相反數(shù)，求m的值．

Answer 1

分析 x、y的值互為相反數(shù)則x+y=0，根據(jù)題意得：$\left\{\begin{array}{l}{2x+y=3}\\{x+y=0}\end{array}\right.$，解方程組求得x和y的值，然后代入x-y=3m求得m的值．

解答 解：x、y的值互為相反數(shù)則x+y=0，
根據(jù)題意得：$\left\{\begin{array}{l}{2x+y=3}\\{x+y=0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=3}\\{y=-3}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=3}\\{y=-3}\end{array}\right.$代入x-y=3m得3-（-3）=3m，
解得：m=2．

點評 本題考查了方程組的解的定義，正確求得x和y的值是解決本題的關(guān)鍵．