Question

15．已知方程组$\left\{\begin{array}{l}{2x+3y=m+3}\\{4x-5y=4m-1}\end{array}\right.$的解满足$\left\{\begin{array}{l}{x＞0}\\{y＜0}\end{array}\right.$，求m的取值范围．

Answer 1

分析 解方程得到用m表示的x、y，根据$\left\{\begin{array}{l}{x＞0}\\{y＜0}\end{array}\right.$得出关于m的不等式组，解之可得答案．

解答 解：解方程$\left\{\begin{array}{l}{2x+3y=m+3}\\{4x-5y=4m-1}\end{array}\right.$，得：$\left\{\begin{array}{l}{x=\frac{17m+12}{22}}\\{y=\frac{-2m+7}{11}}\end{array}\right.$，
由$\left\{\begin{array}{l}{x＞0}\\{y＜0}\end{array}\right.$得$\left\{\begin{array}{l}{\frac{17m+12}{22}＞0}\\{\frac{-2m+7}{11}＜0}\end{array}\right.$，
解得m＞$\frac{7}{2}$．

点评 本题考查的是解二元一次方程组和解一元一次不等式组，根据题意得出关于m的不等式组是解答此题的关键．