Question

16．不等式組$\left\{\begin{array}{l}{x+y≥1}\\{x-2y≤4}\end{array}\right.$的解集為D，下列命題中正確的是（　�。�

• A． ?（x，y）∈D，x+2y≤-1
• B． ?（x，y）∈D，x+2y≥-2
• C． ?（x，y）∈D，x+2y≤3
• D． ?（x，y）∈D，x+2y≥2

Answer 1

分析 化簡(jiǎn)不等式組$\left\{\begin{array}{l}{x+y≥1}\\{x-2y≤4}\end{array}\right.$，即可得出正確的結(jié)論

解答 解：∵不等式組 $\left\{\begin{array}{l}{x+y≥1…①}\\{x-2y≤4…②}\end{array}\right.$，
∴$\left\{\begin{array}{l}{x+y≥1…①}\\{-x+2y≥-4…③}\end{array}\right.$，
∴$\left\{\begin{array}{l}{x+y≥1…①}\\{y≥-1…*}\end{array}\right.$，
∴x+2y≥0；
即x+2y≥-2．
∴若$\left\{\begin{array}{l}{x+y≥1}\\{x-2y≤4}\end{array}\right.$的解集為D時(shí)，?（x，y）∈D，x+2y≥-2成立．
故選：B．

點(diǎn)評(píng) 本題考查了不等式組的解法與應(yīng)用問(wèn)題，也考查了全稱命題與特稱命題的應(yīng)用問(wèn)題，是基礎(chǔ)題目．