Question

1．已知關(guān)于x，y的方程組$\left\{\begin{array}{l}{3x-y=k}\\{2x+3y=2k-1}\end{array}\right.$的解滿足不等式$\left\{\begin{array}{l}{x-4y≥0}\\{5x+2y≥-2}\end{array}\right.$，求滿足條件的k的整數(shù)值．

Answer 1

分析 將k看做已知數(shù)表示出x與y，代入已知不等式組即可求出k的范圍，即可確定整數(shù)值．

解答 解：方程組$\left\{\begin{array}{l}{3x-y=k}\\{2x+3y=2k-1}\end{array}\right.$
解得：$\left\{\begin{array}{l}{x=\frac{5k-1}{11}}\\{y=\frac{4k-3}{11}}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=\frac{5k-1}{11}}\\{y=\frac{4k-3}{11}}\end{array}\right.$代入不等式$\left\{\begin{array}{l}{x-4y≥0}\\{5x+2y≥-2}\end{array}\right.$得：
$\left\{\begin{array}{l}{-11k+12≤0}\\{3k+11≥0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{k≤\frac{12}{11}}\\{k≥-\frac{11}{3}}\end{array}\right.$，
∴$-\frac{11}{3}≤k≤\frac{12}{11}$．
∴k=-3，-2，-1，0，1．

點(diǎn)評 此題考查了二元一次方程組的解，方程組的解即為能使方程組中兩方程成立的未知數(shù)的值，解決本題的關(guān)鍵是求出方程組的解，列出不等式組．