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二元一次方程组专项练习100道

二元一次方程组专项练习100道
二元一次方程组专项练习100道

二元一次方程组练习题100道

一、判断 2、方程组??

?=+-=5

231y x x

y 的解是方程3x -2y =13的一个解( )

4、方程组???????=-++=+++2

5323

473

5

23y x y x ,可以转化为???-=--=+27651223y x y x ( )

5、若(a 2-1)x 2+(a -1)x +(2a -3)y =0是二元一次方程,则a 的值为±1( )

6、若x +y =0,且|x |=2,则y 的值为2 …………( )

7、方程组?

?

?=+-=+81043y x x

m my mx 有唯一的解,那么m 的值为m ≠-5 …………( )

8、方程组??

???=+=+62

3

131

y x y x 有无数多个解 …………( ) 11、若|a +5|=5,a +b =1则3

2-的值为b a ………(

12、在方程4x -3y =7里,如果用x 的代数式表示y ,则4

37y

x +=( ) 13、任何一个二元一次方程都有( ) (A )一个解; (B )两个解; (C )三个解;

(D )无数多个解;

14、一个两位数,它的个位数字与十位数字之和为6,那么符合条件的两位数的个数有( ) (A )5个 (B )6个

(C )7个

(D )8个

15、如果?

?

?=+=-423y x a

y x 的解都是正数,那么a 的取值范围是( )

(A )a <2; (B )34

->a ; (C )3

42<

<-a ; (D )3

4-

17、在下列方程中,只有一个解的是( ) (A )??

?=+=+0

331

y x y x

(B )??

?-=+=+2330

y x y x

(C )?

?

?=-=+4331

y x y x

(D )?

?

?=+=+3331

y x y x

18、与已知二元一次方程5x -y =2组成的方程组有无数多个解的方程是( ) (A )15x -3y =6 (B )4x -y =7

(C )10x +2y =4

(D )20x -4y =3

19、下列方程组中,是二元一次方程组的是( )

(A )??

?

??=+=+9114y x y x

(B )??

?=+=+75

z y y x

(C )?

?

?=-=6231

y x x

(D )?

?

?=-=-1y x xy

y x

20、已知方程组??

?-=+=-1

35

b y ax y x 有无数多个解,则a 、b 的值等于( )

(A )a =-3,b =-14 (B )a =3,b =-7 (C )a =-1,b =9

(D )a =-3,b =14

21、若5x -6y =0,且xy ≠0,则

y

x y

x 3545--的值等于( )

(A )3

2 (B )2

3 (C )1 (D )-1

22、若x 、y 均为非负数,则方程6x =-7y 的解的情况是( ) (A )无解

(B )有唯一一个解 (C )有无数多个解

(D )不能确定

23、若|3x +y +5|+|2x -2y -2|=0,则2x 2-3xy 的值是( ) (A )14

(B )-4

(C )-12

(D )12

24、已知??

?-==24y x 与?

??-=-=52

y x 都是方程y =kx +b 的解,则k 与b 的值为( )

(A )21

=

k ,b =-4 (B )2

1-=k ,b =4

(C )2

1

=k ,b =4 (D )2

1-=k ,b =-4

29、方程|a |+|b |=2的自然数解是_____________; 31、已知方程组??

?-=+=+m

y x ay x 2643

2有无数多解,则a =______,m =______;

33、若4x +3y +5=0,则3(8y -x )-5(x +6y -2)的值等于_________;

34、若x +y =a ,x -y =1同时成立,且x 、y 都是正整数,则a 的值为________; 35、从方程组)0(030

334≠?

?

?=+-=--xyz z y x z y x 中可以知道,x :z =_______;y :z =________;

36、已知a -3b =2a +b -15=1,则代数式a 2-4ab +b 2+3的值为__________;

45、?????=-+=+-=-+3

53513

43z y x z y x z y x 46、??

?

??=+-==30325:3:7:4:z y x z x y x ;

48、使x +4y =|a |成立的x 、y 的值,满足(2x +y -1)2+|3y -x |=0,又|a |+a =0,求a 的值;

49、代数式ax 2+bx +c 中,当x =1时的值是0,在x =2时的值是3,在x =3时的值是28,试求出这个代数式;

52、a 、b 、c 取什么数值时,x 3-ax 2+bx +c 程(x -1)(x -2)(x -3)恒等?

53、m 取什么整数值时,方程组?

??=-=+024

2y x my x 的解:

(1)是正数;

(2)是正整数?并求它的所有正整数解。

54、试求方程组?

??-=---=-6|2||

5|7|2|y x y x 的解。

55、汽车从甲地到乙地,若每小时行驶45千米,就要延误30分钟到达;若每小时行驶50千米,那就可以提前30分钟到达,求甲、乙两地之间的距离及原计划行驶的时间?

56、某班学生到农村劳动,一名男生因病不能参加,另有三名男生体质较弱,教师安排他们与女生一起抬土,两人抬一筐土,其余男生全部挑土(一根扁担,两只筐),这样安排劳动时恰需筐68个,扁担40根,问这个班的男女生各有多少人?

57、甲、乙两人练习赛跑,如果甲让乙先跑10米,那么甲跑5秒钟就可以追上乙;如果甲让乙先跑2秒钟,那么甲跑4秒钟就能追上乙,求两人每秒钟各跑多少米?

58、甲桶装水49升,乙桶装水56升,如果把乙桶的水倒入甲桶,甲桶装满后,乙桶剩下的水,恰好是乙桶容量的一半,若把甲桶的水倒入乙桶,待乙桶装满后则甲桶剩下的水恰好是甲桶容量的

3

1,求这两个水桶的容量。

59、甲、乙两人在A地,丙在B地,他们三人同时出发,甲与乙同向而行,丙与甲、乙相向而行,甲每分钟走100米,乙每分钟走110米,丙每分钟走125米,若丙遇到乙后10分钟又遇到甲,求A、B两地之间的距离。

二元一次方程组练习题100道(卷二)

6.方程组

43

235

x y k

x y

-=

?

?

+=

?

的解与x与y的值相等,则k等于()

13.已知│x-1│+(2y+1)2=0,且2x-ky=4,则k=_____.14.二元一次方程x+y=5的正整数解有______________.

15.以

5

7

x

y

=

?

?

=

?

为解的一个二元一次方程是_________.

18.如果(a-2)x+(b+1)y=13是关于x,y的二元一次方程,则a,b满足什么条件?

23.方程组25

28x y x y +=??

-=?的解是否满足2x -y=8?满足2x -y=8的一对x ,y 的值是否是

方程组2528x y x y +=??-=?

的解?

24.(开放题)是否存在整数m ,使关于x 的方程2x+9=2-(m -2)x 在整数范围内

有解,你能找到几个m 的值?你能求出相应的x 的解吗?

14、若()4360,2700,x y z x y z xyz --=+-=≠求代数式222

222

522310x y z x y z +---的值。

23、古算题:“我问开店李三公,众客都来到店中,一房七客多七客,一房九客一房空.问多少房间多少客?”(题目大意是:一些客人到李三公的店中住宿,若每间房里住7人,就分有7人没地方住;若每间房住9人,则空出一间房.问有多少房间多少客人.)

20、用如图1中的长方形和正方形纸板做侧面和底面,做成如图2的竖式和横式两种无盖纸盒。现在仓库里有1000张正方形纸板和2000张长方形纸板,问两种纸盒各做多少个,恰好将库存的纸板用完?

一、1、√; 2、√; 3、×; 4、×; 5、×; 6、×; 7、√; 8、√; 9、×;10、×; 11、×;

12、×;

二、13、D ; 14、B ; 15、C ; 16、A ; 17、C ; 18、A ;

19、C ; 20、A ;21、A ; 22、B ; 23、B ; 24、A ; 三、25、4

7,8,?

?

?==14

y x ; 26、2;

27、4

12

5+=

y x ; 28、a =3,b =1;

29、??

?==2

b a ???==1

1b a ?

??==02

b a 30、2

1

; 31、3,-4 32、1; 33、20; 34、a 为大于或等于3的奇数;

35、4:3,7:9

36、0;

五、47、???-=-=+2941358y x y x ,???

????=

=231792

107y x ;

48、a =-1 49、11x 2

-30x +19;

50、3

1

=a ;

51、2

3

=

a ,

b =±3 52、a =6, b =11,

c =-6;

53、(1)m 是大于-4的整数,(2)m =-3,-2,0,??

?==48y x ,???==24y x ,?

??==12

y x ; 54、??

?=-=91y x 或?

??==95

y x ; 六、55、A 、B 距离为450千米,原计划行驶9.5小时;

56、设女生x 人,男生y 人,???????=?-++=-++68

2)4(2

34042

3

y x y x ???==)(32)(21人人y x

57、设甲速x 米/秒,乙速y 米/秒 ??

?==-y x y x 641055 ?

??==)/(4)

/(6秒米秒米y x

58、甲的容量为63升,乙水桶的容量为84升; 59、A 、B 两地之间的距离为52875米; 60、所求的两位数为52和62。 6.B

13.4 解析:由已知得x-1=0,2y+1=0,

∴x=1,y=-1

2

,把

1

1

2

x

y

=

?

?

?

=-

??

代入方程2x-ky=4中,2+

1

2

k=4,∴k=1.

14.解:

1234

4321 x x x x

y y y y

====????

????====????

解析:∵x+y=5,∴y=5-x,又∵x,y均为正整数,

∴x为小于5的正整数.当x=1时,y=4;当x=2时,y=3;当x=3,y=2;当x=4时,y=1.

∴x+y=5的正整数解为

1234

4321 x x x x

y y y y

====????

????====????

15.x+y=12 解析:以x与y的数量关系组建方程,如2x+y=17,2x-y=3等,此题答案不唯一.

18.解:∵(a-2)x+(b+1)y=13是关于x,y的二元一次方程,∴a-2≠0,b+1≠0,?∴a≠2,b≠-1

解析:此题中,若要满足含有两个未知数,需使未知数的系数不为0.

(?若系数为0,则该项就是0)

23.解:满足,不一定.

解析:∵

25

28

x y

x y

+=

?

?

-=

?

的解既是方程x+y=25的解,也满足2x-y=8,?

∴方程组的解一定满足其中的任一个方程,但方程2x-y=8的解有无数组,

如x=10,y=12,不满足方程组

25 28

x y

x y

+=

?

?

-=

?

24.解:存在,四组.∵原方程可变形为-mx=7,

∴当m=1时,x=-7;m=-1时,x=7;m=?7时,x=-1;m=-7时x=1.

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————————————————————————————————作者: ————————————————————————————————日期:

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