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【323577】2023七年级数学上册 第3章 一次方程与方程组 建立二元一次方程组练习(新版)沪科版

时间:2025-01-15 19:25:14 作者: 字数:3591字
简介:


建立二元一次方程组

(30分钟 50)

一、选择题(每小题4,12)

1.下列方程中,是二元一次方程的是(  )

A.3x2-2y=4 B.6 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> x+y+ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 9z=0

C. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> +4y=6 D.4x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

2. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 为解的二元一次方程组是(  )

A. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> B. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

C. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> D. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

3.(2013·广州中考)已知两数x,y之和是10,xy3倍大2,则下面所列方程组正确的是(  )

A. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> B. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

C. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> D. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

二、填空题(每小题4,12)

4.请写出一个二元一次方程组        ,使它的解是 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

5.方程(k2-1)x2+(k+1)x+2ky=k+3,k=    ,它为一元一次方程;k=

    ,它为二元一次方程.

6. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 母亲节那天,很多同学给妈妈准备了鲜花和礼盒.从信息中可知,若设鲜花x/,礼盒y/,则可列方程组为    .

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

三、解答题(26)

7.(8)下列各组数据中哪些是方程3x-2y <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> =11的解?哪些是方程2x+3y=16的解?哪些是方程组 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 的解?为什么?

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 8.(8)(1) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 是方程2x+y=0的解,6a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> + <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 3b+2的值.

(2) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 是方程3x-y=1的解,6a-2b+3的值.

【拓展延伸】

9.(10)为民医疗器械经销部经营甲、乙两种医疗器械,甲器械每台2万元,乙器械每台5万元,今年厂方给经销部规定了24万元的营销任务,那么该经 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 销部要想刚好完成任务,有哪些销售方案可选择?若乙医疗器械的利润是甲医疗器械的3,那么你觉得选 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 择哪个方案更好些?




答案解析 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

1.【解析】选D.4x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 含有两个未知数x,y,并且含x,y项的次数都是1,是二元一次方程.选项A有二次项,选项B有三个未知数,选项C分母中有未知数,A,B,C都不是二元一次方程.

2.【解析】选D. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 分别代入四个方程组中,只有D中的两个方程同时成立.

3.【解析】选C.由题意知,x+y=10,x-3y=2,x=3y+2,所以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

4.【解析】以 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 为解的二元一次方程有无数个,x+y=1,x-y=3,x+2y=0,只要满足x=2,y=-1即可.然后从中选两个方程,但是这两个方程的对应项的系数不能成倍数关系.

答案: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> (答案不唯一)

5.【解析】无论是一元一次方程还是二元一次 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 方程,都不可能有二次项,所以k2-1=0,k=±1.k=-1,原方程为-2y=2是一元一次方程;k=1,原方程为x+y=2为二元一次方程.

答案 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> :-1 1

6.【解析】一束鲜花x,一盒礼盒y,由一束鲜花和两盒礼盒 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>55,:x+2y=55;由两束鲜花和3盒礼盒共90,2x+3y=90, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

答案: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a>

7.【解析】①②是方程3x-2y=11的解.②③是方程2x+3y=16的解.②是方程组 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 的解.

因为方程组的解必须是方程组中两个方程的公共解.

8.【解析】(1) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 代入方程2x+y=02a+b=0,两边同时乘以3:6a+3b=0,所以6a+3b+2=2.

(2) <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> 代入3x-y=13a-b=1,

6a-2b+3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> =2(3a-b)+3=5.

【归纳整合】解决本题的方法为整体代入法,将含a,b的式子整体代入,使得整个求解过程更加简便,在解决整体代入法求值问题时,要多观察式子的特点,合理运用整体代入法.

9.【解析】设销售甲医疗器械x,乙医疗器械y,根据题意,2x+5y=24.因为x,y都是非负整数,所以x= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> =12-2y- <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/860/" title="建立" class="c1" target="_blank">建立</a> .y=0,x=12;y=2,x=7;y=4,x=2.所以销售方案有三种:方案一:销售甲器械12,乙器械0;方案二:销售甲器械7,乙器械2;方案三:销售甲器械2,乙器械4.

设甲医疗器械的利润为a(a>0),则方案一的利润为12a+0×3a=12a();方案二的利润为7a+2×3a=13a();方案三的利润为2a+4×3a=14a().因为14a>13a>12a,所以选择方案三更好些.

3