已知关于
,
的方程组
(
是常数).
(1)当
时,则方程组可化为
.
①请直接写出方程
的所有非负整数解.
②若该方程组的解也满足方程
,求
的值.
(2)当
时,如果方程组有整数解,求整数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0dc3ee14e46aa290d53004d57203c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4cb68c20fd72b89c9e1ed6d3aab710.png)
①请直接写出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff16f02559e1312c183861c5526e560.png)
②若该方程组的解也满足方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
22-23七年级下·江苏盐城·阶段练习 查看更多[7]
江苏省盐城市滨海县一中教育集团2022-2023学年七年级下学期5月月考(第二阶段调研)数学试题(已下线)第02讲 解题技巧专题:二元一次方程组中易错及含参数问题(6类热点题型讲练)-【帮课堂】2023-2024学年八年级数学上册同步学与练(北师大版)(已下线)专题5.5 二元一次方程组章末拔尖卷-2023-2024学年八年级数学上册举一反三系列(北师大版)05-一次方程(组)及其应用8.3实际问题与二元一次方程组(已下线)专题8.19 二元一次方程组(全章分层练习)(培优练)-2023-2024学年七年级数学下册基础知识专项突破讲与练(人教版)(已下线)专题10.18 二元一次方程组(全章分层练习)(提升练)-2023-2024学年七年级数学下册基础知识专项突破讲与练(苏科版)
更新时间:2023-08-29 21:15:00
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【推荐1】已知关于x,y的二元一次方程
(a,b为常数且
)
(1)若
,
,
①若x,y为正整数,该方程的解为______________;
②若
,计算
.
(2)若
和
是该方程的两组解,
,
,且
,
,请比较
和
大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edfef76505153783aa49286949e6604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82986ab38a4ae58593191ccae2a44f62.png)
①若x,y为正整数,该方程的解为______________;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4f3ea707431e69ce7f67f20b09c5ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1485073e6b4e9a72579ad8125d363326.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ca338156a08388b2e441053410473c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5494ee24d70ffc9d9ca797222c55a7da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95dfc2da99a73f088189fcd377bb3593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b9871fdb518c0a38b1fdd2cdb9b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9786020d56219563c0d3bfdea638a3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c44826e58f11a58d3a6c233fc5df2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215b1424b299b737554386b090af8316.png)
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【推荐2】为了探究函数在图象不明的情况下,函数值的变化情况,我们可以这样定义:如果点
、
在函数的图象上,那么我们把
称为该函数的“单位铅直高”.例如:函数
,当
时,
;当
时,
,
,则函数
“单位铅直高”![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4620140087776629ef815015bdcd97.png)
(1)正比例函数
的“单位铅直高”
______;
(2)若点
,
在反比例函数
的图象上,当这个反比例函数的“单位铅直高”
,求m的值;
(3)已知二次函数
,求这个二次函数的“单位铅直高”t的最小值;
(4)求反比例函数
的“单位铅直高”t的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d971e9aa34dde8c160dc925dcb5b7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7abe648bc9fbdfceaf89b2c9bc6402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b5f5d37acd5cae8f2ac9ebd7bf3999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd1dcfe0c394b37a58b20c3b8123d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd50b25a1accb91acb3df0ee32796a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fea1ca1d19a78168a3b9fb0f2fa21f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7a7989f3e2d60881c0a8fec7256412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdcd0eb2fab5060462f7544393679a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd1dcfe0c394b37a58b20c3b8123d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4620140087776629ef815015bdcd97.png)
(1)正比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4407788e4dc88210bca71a2551d4f2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae976c4bacfaf87fa09049537a48205e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8064bc28205a92a1371a577ec13d5ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa6dd02ca8f212c19ce376ee87fa722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
(3)已知二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572359034257e983b7b99d4e74f54cc8.png)
(4)求反比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef854dfcbba9b7dedc1bc52f6332b011.png)
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【推荐3】把一个各个数位的数值互不相等且均不为0的正整数重新排列各数位上的数字,必可得到一个最大数和一个最小数,用最大数减去最小数可得原数的极差数,记为P(t).例如,254的极差数P(254)=542﹣245=297,3245的极差数P(3245)=5432﹣2345=3087
(1)P(326)= ;P(6152)= ;
(2)已知一个三位数
(其中a>b>3)的极差数P
=495,且这个三位数各数位上的数字之和为6的倍数,求这个三位数;
(3)若一个两位数m=11a+b,一个三位数n=111a+b+200,(其中1≤a≤4,1≤a+b≤9,a,b为正整数),交换三位数n的个位数字和百位数字得到新数n′,当m的个位数字的3倍与n′的和能被13整除时,称这样的两个数m和n为“组合数对”,求所有“组合数对”中P(n)的最大值.
(1)P(326)= ;P(6152)= ;
(2)已知一个三位数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ed868790a747c4b9764b2fcb84f411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a1832480fc2430521d6ba0868b646d.png)
(3)若一个两位数m=11a+b,一个三位数n=111a+b+200,(其中1≤a≤4,1≤a+b≤9,a,b为正整数),交换三位数n的个位数字和百位数字得到新数n′,当m的个位数字的3倍与n′的和能被13整除时,称这样的两个数m和n为“组合数对”,求所有“组合数对”中P(n)的最大值.
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【推荐1】已知
,
都是关于
,
的二元一次方程
的解,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4395074827b26a91d61d4c5e60fed319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91120b4b1dd8fe9ea1fe97bf3bfc0d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07565f10847840e0fb07b05218ad17fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577a16745c4b04ba859ca853c268d24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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【推荐2】已知二元一次方程
(a,b均为常数,且a≠0).
(1)当a=3,b=﹣4时,用x的代数式表示y;
(2)若
是该二元一次方程的一个解,
①探索a与b关系,并说明理由;
②无论a、b取何值,该方程有一组固定解,请求出这组解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0e90715630b6eaf007fd0d78548b23.png)
(1)当a=3,b=﹣4时,用x的代数式表示y;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e5a5685d655f69858ea6a2098556e.png)
①探索a与b关系,并说明理由;
②无论a、b取何值,该方程有一组固定解,请求出这组解.
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【推荐1】在平面直角坐标系中,
为坐标原点,点A的坐标为
,点
的坐标为
,点
的坐标为
,其中
,
,
满足方程组
.
(1)若
,求
的面积;
(2)连接
,线段
沿
轴方向平移到线段
,线段
扫过的面积为15,则点
平移后对应点
的纵坐标为________;
(3)连接
,
,
,若
的面积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1f08e04cf0b6a9afea66ce590ba00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff091ae80d01c44df1dd53f7de8d26c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05717f3f86f5f0a83a4770db944e3954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ead31be63a9d16eb3745b33f9c85a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b97bb18e5ca34d22b5e827316a122a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9904bd1c9cc73cc01e89ea7793e8cabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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【推荐2】阅读下列材料,解答下面的问题:我们知道方程
有无数个解,但在实际问题中往往只需求出其正整数解.例:由
,得:
(
、
为正整数).要使
为正整数,则
为正整数,可知:
为3的倍数,从而
,代入
.所以
的正整数解为
.问题:
(1)请你直接写出方程
的正整数解___________.
(2)若
为自然数,则求出满足条件的正整数
的值.
(3)关于
,
的二元一次方程组
的解是正整数,求整数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aadc211ecf57ef98bfc545faa9fe29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aadc211ecf57ef98bfc545faa9fe29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67cca83f2c9e087566630d21d293cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66207e85c3cb83562d533aca187584e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8158d9ec9dd2ae8d41f1d7807c07dfc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/379e707a1186f91826b745bbd4e3be7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aadc211ecf57ef98bfc545faa9fe29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ff2de37f9b1dec2ba9287f76aeda05.png)
(1)请你直接写出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7509cfcb38441e750107be35ffd54144.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4cf1be4dcb36bb859e655cf76bc625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad37dede5ccff434ce51a2ba2b1184ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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【推荐1】如图,数轴上两点A、B对应的数分别是-1,1,点P是线段AB上一动点,给出如下定义:如果在数轴上存在动点Q,满足|PQ|=2,那么我们把这样的点Q表示的数称为连动数,特别地,当点Q表示的数是整数时我们称为连动整数.
(2)若k使得方程组
中的x,y均为连动数,求k所有可能的取值;
(3)若关于x的不等式组
的解集中恰好有4个连动整数,求这4个连动整数的值及a的取值范围.
(2)若k使得方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf090c61aa85104765bdc71660ac41e9.png)
(3)若关于x的不等式组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be14e099b5e9d8b00b2d20585d1d20b.png)
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【推荐2】已知关于x,y的方程组
的解都为正数.
(1)当a=2时,解此方程组;
(2)求a的取值范围;
(3)已知a+b=4,且b>0,z=2a-3b,求z的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0389c48218e1287bc06a8f009289f48b.png)
(1)当a=2时,解此方程组;
(2)求a的取值范围;
(3)已知a+b=4,且b>0,z=2a-3b,求z的取值范围.
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