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【323576】2023七年级数学上册 第3章 一次方程与方程组 加减消元法(第2课时)练习(新版)沪

时间:2025-01-15 19:25:11 作者: 字数:2742字
简介:


加减消元法(2课时)

(30分钟 50)

一、选择题(每小题4,12)

1.(2013·凉山州中考)已知方程组 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>x+y的值为(  )

A.-1 B.0 C.2 D.3

2.方程组 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 将②×3-①×2(  )

A.-3y=2 B.4y+1=0

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> C.y=0 D.7y=-8

3.小明在解关于x,y的二元一次方程组 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 时得到了正确结果 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 后来发现“⊗”“⊕” <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 处被墨水污损了,请你帮他找出“⊗”“⊕”处的值分别是(  )

A.⊗=1,⊕=1 B.⊗=2,⊕=1

C.⊗=1, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> ⊕=2 D.⊗=2,⊕=2

二、填空题(每小题4,12)

4.若单项式3xm+2ny-4x3y3m-2n的和为单项式,m=    ,n=    .

5.已知代数式x2+bx+c,x=1 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> ,其值是8;x=-1,其值为-2,b=    ,c=    .

6.方程组 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 的解应为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 一个同学把c看错了.因此解得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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+b+c=    .

三、解答题 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> (26)

7.(8)(2013·黄冈中考)解方程组:

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

8.(8)若关于x,y的方程3 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> x-2ny=m-n有一个解为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 此时mn的一半大1,m,n的值分别为多少?

【拓展延伸】

9.(10)学过了二元一次方程组的解法后,课堂上老师又写出了一个题目:你会解这 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 个方程组吗?

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

小明、小刚、小芳争论了一会儿, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 们分别写出了一种方法.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>:把原方程组整理得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

×4-③30y=-210,所以y=-7,

y=-7代入③得8x=104,所以x=13,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

小刚: <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> =m, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> =n, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

+④m=1,③-④n=2.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/16/" title="课时" class="c1" target="_blank">课时</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>

③④组成方程组

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/16/" title="课时" class="c1" target="_blank">课时</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/16/" title="课时" class="c1" target="_blank">课时</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>

老师看过,非常高兴,特别是小刚,方法独特,像小刚这种解方程组的方法叫换元法,你能用换元法解下 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 列方程组吗?

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>



答案解析

1.【解析】选D. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 对①变形,y=4-2x③,将③代入②中,x+2(4-2x)=5,去括号,x+8-4x=5,化简,x=1,x=1代入②中,y=2.x+y=3.

2.【解析】选C.②×3:6x-9y=12 ③,

×2:6x-10y=12 ④,

-④:y=0.

3.【解析】选B. <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 代入方程组,两方程相加,x=⊕=1,x=y=1代入方程x+⊗y=3,1+⊗=3,⊗=2.

4.【解析】由题意得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 解得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

答案:1 1

5.【解析】 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 由题意得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

解得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

答案:5 2

6.【解析】把 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 代入方程组 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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/16/" title="课时" class="c1" target="_blank">课时</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> 由②得c=7, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 代入ax+by=267a+3b=26③,①③组成方程组 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

4a-2b=26可转化为b=2a-13,b=2a-13代入7a+3b=26,a=5.

a= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 5代入③得,b=-3.所以a=5,b=-3,c=7.

所以a+b <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> +c=5+(-3)+7=9.

答案:9

7.【解析】原方程组整理得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

由①得,x=5y-3 ③,

将③代入②得,

25y-15-11y=-1,

14y=14,y=1,

y=1代入③得x=2.

所以原方程组的解为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

8.【解析】将 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 代入3x-2ny=m-n,

6+2n=m-n,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> mn的一半大1m- <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> n=1.

联立得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 解得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

所以m的值为0,n的值为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> -2.

9.【解析】设 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> =b,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

+②a=3,

-②b=-2,

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

所以 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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> 解得 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

所以原方程组的解为 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</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>

5