不等式組經(jīng)典題目及答案一、選擇題（共30分）1.（6分）若不等式組\(\begin{cases}x+y\leq6\\x-y\geq0\end{cases}\)的解集為\(\{(x,y)|x\geq0,y\leq3\}\)，則以下哪個選項是正確的？A.\(x\leq3\)B.\(y\leq3\)C.\(x\geq3\)D.\(y\geq3\)答案：B2.（6分）若不等式組\(\begin{cases}x+y\geq4\\x-y\leq2\end{cases}\)的解集為\(\{(x,y)|1\leqx\leq3,1\leqy\leq3\}\)，則以下哪個選項是正確的？A.\(x\leq1\)B.\(y\leq1\)C.\(x\geq3\)D.\(y\geq3\)答案：C3.（6分）若不等式組\(\begin{cases}x+2y\geq4\\2x+y\leq6\end{cases}\)的解集為\(\{(x,y)|1\leqx\leq2,1\leqy\leq2\}\)，則以下哪個選項是正確的？A.\(x\leq1\)B.\(y\leq1\)C.\(x\geq2\)D.\(y\geq2\)答案：C4.（6分）若不等式組\(\begin{cases}x-y\geq1\\3x+y\leq9\end{cases}\)的解集為\(\{(x,y)|1\leqx\leq3,-1\leqy\leq2\}\)，則以下哪個選項是正確的？A.\(x\leq1\)B.\(y\leq-1\)C.\(x\geq3\)D.\(y\geq2\)答案：D5.（6分）若不等式組\(\begin{cases}x^2+y^2\leq9\\x+y\geq3\end{cases}\)的解集為\(\{(x,y)|0\leqx\leq3,0\leqy\leq3\}\)，則以下哪個選項是正確的？A.\(x\leq0\)B.\(y\leq0\)C.\(x\geq3\)D.\(y\geq3\)答案：C二、填空題（共30分）1.（6分）解不等式組\(\begin{cases}x+y\leq5\\x-y\geq1\end{cases}\)，得到解集為\(\{(x,y)|1\leqx\leq3,2\leqy\leq4\}\)。答案：\(\{(x,y)|1\leqx\leq3,2\leqy\leq4\}\)2.（6分）解不等式組\(\begin{cases}2x+y\geq6\\x-2y\leq0\end{cases}\)，得到解集為\(\{(x,y)|2\leqx\leq3,1\leqy\leq2\}\)。答案：\(\{(x,y)|2\leqx\leq3,1\leqy\leq2\}\)3.（6分）解不等式組\(\begin{cases}x^2+y^2\leq16\\x+y\geq4\end{cases}\)，得到解集為\(\{(x,y)|0\leqx\leq4,0\leqy\leq4\}\)。答案：\(\{(x,y)|0\leqx\leq4,0\leqy\leq4\}\)4.（6分）解不等式組\(\begin{cases}x^2-y^2\geq4\\x+y\leq5\end{cases}\)，得到解集為\(\{(x,y)|1\leqx\leq3,1\leqy\leq3\}\)。答案：\(\{(x,y)|1\leqx\leq3,1\leqy\leq3\}\)5.（6分）解不等式組\(\begin{cases}x^2+2y^2\leq18\\2x-y\geq2\end{cases}\)，得到解集為\(\{(x,y)|1\leqx\leq3,1\leqy\leq2\}\)。答案：\(\{(x,y)|1\leqx\leq3,1\leqy\leq2\}\)三、解答題（共40分）1.（10分）解不等式組\(\begin{cases}x+y\leq8\\2x-y\geq4\end{cases}\)，并寫出解集。解：首先解第一個不等式\(x+y\leq8\)，得到\(y\leq8-x\)。然后解第二個不等式\(2x-y\geq4\)，得到\(y\leq2x-4\)。將兩個不等式結(jié)合起來，得到解集為\(\{(x,y)|2\leqx\leq4,4-2x\leqy\leq8-x\}\)。答案：\(\{(x,y)|2\leqx\leq4,4-2x\leqy\leq8-x\}\)2.（10分）解不等式組\(\begin{cases}x^2+y^2\leq25\\x-y\geq0\end{cases}\)，并寫出解集。解：首先解第一個不等式\(x^2+y^2\leq25\)，得到圓心在原點，半徑為5的圓內(nèi)的所有點。然后解第二個不等式\(x-y\geq0\)，得到直線\(x=y\)右側(cè)的所有點。將兩個不等式結(jié)合起來，得到解集為圓內(nèi)且在直線\(x=y\)右側(cè)的所有點。答案：圓心在原點，半徑為5的圓內(nèi)且在直線\(x=y\)右側(cè)的所有點。3.（10分）解不等式組\(\begin{cases}3x+4y\geq12\\2x-y\leq4\end{cases}\)，并寫出解集。解：首先解第一個不等式\(3x+4y\geq12\)，得到\(y\geq3-\frac{3}{4}x\)。然后解第二個不等式\(2x-y\leq4\)，得到\(y\geq2x-4\)。將兩個不等式結(jié)合起來，得到解集為\(\{(x,y)|1\leqx\leq4,3-\frac{3}{4}x\leqy\leq2x-4\}\)。答案：\(\{(x,y)|1\leqx\leq4,3-\frac{3}{4}x\leqy\leq2x-4\}\)4.（10分）解不等式組\(\begin{cases}x^2-y^2\leq9\\x+2y\geq6\end{cases}\)，并寫出解集。解：首先解第一個不等式\(x^2-y^2\leq9\)，得到雙曲線\(x^2-y^2=9\)內(nèi)部的所有點。然后解第二個不等式\(x+2y\geq6