二元一次方程不等式10道 需要过程 求10道简单二元二次方程组数学题目及其答案,10道二元一次方...
\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u548c\u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f\u4e0d\u7b49\u5f0f\u7ec4\u5404100\u9053\u8981\u8fc7\u7a0b\u548c\u7b54\u6848\u4e3a\u4ec0\u4e48\u662f100\u9053
1) 66x+17y=3967
25x+y=1200
\u7b54\u6848\uff1ax=48 y=47
(2) 18x+23y=2303
74x-y=1998
\u7b54\u6848\uff1ax=27 y=79
(3) 44x+90y=7796
44x+y=3476
\u7b54\u6848\uff1ax=79 y=48
(4) 76x-66y=4082
30x-y=2940
\u7b54\u6848\uff1ax=98 y=51
(5) 67x+54y=8546
71x-y=5680
\u7b54\u6848\uff1ax=80 y=59
(6) 42x-95y=-1410
21x-y=1575
\u7b54\u6848\uff1ax=75 y=48
(7) 47x-40y=853
34x-y=2006
\u7b54\u6848\uff1ax=59 y=48
(8) 19x-32y=-1786
75x+y=4950
\u7b54\u6848\uff1ax=66 y=95
(9) 97x+24y=7202
58x-y=2900
\u7b54\u6848\uff1ax=50 y=98
(10) 42x+85y=6362
63x-y=1638
\u7b54\u6848\uff1ax=26 y=62
(11) 85x-92y=-2518
27x-y=486
\u7b54\u6848\uff1ax=18 y=44
(12) 79x+40y=2419
56x-y=1176
\u7b54\u6848\uff1ax=21 y=19
(13) 80x-87y=2156
22x-y=880
\u7b54\u6848\uff1ax=40 y=12
(14) 32x+62y=5134
57x+y=2850
\u7b54\u6848\uff1ax=50 y=57
(15) 83x-49y=82
59x+y=2183
\u7b54\u6848\uff1ax=37 y=61
(16) 91x+70y=5845
95x-y=4275
\u7b54\u6848\uff1ax=45 y=25
(17) 29x+44y=5281
88x-y=3608
\u7b54\u6848\uff1ax=41 y=93
(18) 25x-95y=-4355
40x-y=2000
\u7b54\u6848\uff1ax=50 y=59
(19) 54x+68y=3284
78x+y=1404
\u7b54\u6848\uff1ax=18 y=34
(20) 70x+13y=3520
52x+y=2132
\u7b54\u6848\uff1ax=41 y=50
\u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f\uff08\u7ec4\uff09
\uff081\uff0998/X>7
98/(X+3)<7
\u7b54\uff1a11<X<14
\uff082\uff090\u22643x+8-(x-1)*5<3
\u7b54\uff1a5<x\u22646
\uff083\uff091.1*30/22<1.1+x<1.1*30/20
\u7b54\uff1a0.4<x<0.55
\uff084\uff092x\uff0d1<4x\uff0b13
\u7b54\uff1a x>\uff0d7.
\uff085\uff092\uff085x\uff0b3\uff09\u2264x\uff0d3\uff081\uff0d2x\uff09\uff0c
\u7b54\uff1ax\u2264\uff0d3.
\uff086\uff09 2\uff08x\uff0b4\uff09\uff0d3\uff083x\uff0d1\uff09>6\uff0c
\u7b54\uff1ax<7/5
\uff087\uff092x-3x-3\uff1c6
\u7b54\uff1ax\uff1c-9
\uff088\uff092(x-1)\uff1e3(x-1)-x-5
\u7b54\uff1a\u65e0\u89e3
\uff089\uff092x+3<-1
\u7b54\uff1ax<-2
\uff0810\uff0950+x<2x-30
\u7b54\uff1ax>80
\uff0811\uff09x+1\uff1e2x-1
\u7b54\uff1ax<2
\uff0812\uff090.5x+12-0.5<8.5
\u7b54\uff1ax<-6
\uff0813\uff092x+5>1
\u7b54\uff1ax>-2
\uff0814\uff096x+1>25
\u7b54\uff1ax>4
\uff0815\uff09x+15<22-2x
\u7b54\uff1ax<7/3
\uff0816\uff095x+3>6
\u7b54\uff1ax>3/5
\uff0817\uff099x+21>(x+1)2
\u7b54\uff1ax>-7/19
\uff0818\uff09(x+1)3>(x-10)2
\u7b54\uff1ax>-23
\uff0819\uff0920x>40
\u7b54\uff1ax>2
\uff0820\uff0915x+20<7x+10
\u7b54\uff1ax<-4/5
\u8bf7\u91c7\u7eb3\u7b54\u6848\uff0c\u652f\u6301\u6211\u4e00\u4e0b\u3002
1.
x^2-5x-y^2-5y=0
x^2+xy+y^2=49
\u6839\u636e\u5f0f\u5b501\u5f97\u77e5\uff08x-2.5\uff09^2=(y+2.5)^2
\u89e3\u5f97x-y=5\u6216\u8005x+y=0
1.\u82e5x-y=5
\u90a3\u5e26\u51652\u5f0f\uff0c\u5f97y^2+5y-8=0,\u6c42\u0394=5^2+4X2X8=89
\u6c42\u51fay\u67092\u4e2a\u6839\uff0c\u5206\u522b\u662f[-5+\u6839\u53f789]/2\u548c[-5-\u6839\u53f789]/2
x\u5bf9\u5e94\u5206\u522b\u4e3a[5+\u6839\u53f789]/2\u548c[5-\u6839\u53f789]/2
2,\u82e5x+y=0
y^2=49,y\u53ef\u53d67\u548c-7
\u90a3x\u5206\u522b\u4e3a-7\u548c7
\u4e00\u51714\u7ec4\u89e3\uff0c\u5982\u4e0a\u6240\u8bf4
2.
x^2+y^2=45
(x+y)^2-2xy=45
(x+y)^2=85 x+y=\u00b1\u221a85
(x-y)^2+2xy=45
(x-y)^2=5 x-y=\u00b1\u221a5
\u4e0ex+y=\u00b1\u221a85\u8054\u7acb\u6c42\u89e3
x=(\u221a85+\u221a5)/2 y=(\u221a85-\u221a5)/2
\u6216x=(\u221a85-\u221a5)/2 y=(\u221a85+\u221a5)/2
\u6216x=-(\u221a85+\u221a5)/2 y=-(\u221a85-\u221a5)/2
\u6216x=(-\u221a85+\u221a5)/2 y=(-\u221a85-\u221a5)/2
3.
x^2-xy+y^2=3,2x^2-xy-y^2=5
5x^2-5xy+5y^2=15
6x^2-3xy-3y^2=15
\u4e24\u5f0f\u5b50\u76f8\u51cf
x^2+2xy-8y^2=0
(x+4y)(x-2y)=0
x=2y\u6216\u8005x=-4y
\u5f53x=2y\u65f6
\u4ee3\u5165\u7b2c\u4e00\u4e2a\u5f0f\u5b50\u6709
4y^2-2y^2+y^2=3
3y^2=3
y=\u00b11
\u6b64\u65f6x=2\uff0cy=1\u6216\u8005x=-2\uff0cy=-1
\u5982\u679cx=-4y\u4ee3\u5165\u5f0f\u5b50
16y^2+4y^2+y^2=3
y^2=1/7
y=\u00b1\u6839\u53f77/7
x=4\u6839\u53f77/7\uff0cy=-\u6839\u53f77/7
\u6216\u8005x=-4\u6839\u53f77/7\uff0cy=\u6839\u53f77/7
\u7efc\u4e0a
x=4\u6839\u53f77/7\uff0cy=-\u6839\u53f77/7
\u6216\u8005x=-4\u6839\u53f77/7\uff0cy=\u6839\u53f77/7
\u6216\u8005
x=2\uff0cy=1\u6216\u8005x=-2\uff0cy=-1
4.
xy-2y-x+2=(x-2)y-(x-2)=0,y=1\u6216x=2
\u8bbey=1\uff0c\u5219x^2-3xy+5y-5=x^2-3x+5-5=x^2-3x=x*\uff08x-3\uff09=0\u6240\u4ee5x=0\u6216x=3
\u8bbex=2\uff0c\u5219x^2-3xy+5y-5=4-6y+5y-5=0\uff0cy=1
\u6240\u4ee5\u6709x1=0,y1=1
x2=3,y2=1
x3=2,y3=1
5.
xy+x+y=11
x^2y+xy^2=30
xy(x+y)=30
xy,x+y\u4e3a\u65b9\u7a0b
x^2-11x+30=0\u4e24\u4e2a\u6839
(x-5)(x-6)=0
xy=5,x+y=6\u6216xy=6,x+y=5
1)xy=5,x+y=6
x,y\u662f\u65b9\u7a0bx^2-6x+5=0\u4e24\u4e2a\u6839
x=1,y=5\u6216x=5,y=1
2)xy=6,x+y=5
x,y\u662f\u65b9\u7a0bx^2-5x+6=0\u4e24\u4e2a\u6839
x=2,y=3\u6216x=3,y=2
\u6240\u4ee5\u65b9\u7a0b\u7ec4\u89e3\uff1a
x=1,y=5
\u6216x=5,y=1
\u6216x=2,y=3
\u6216x=3,y=2
6.
x²-y²=-21
2xy=20
\u7531x²-y²=-21\u5f97y²-x²=21\u2460
\u75312xy=20\u5f97xy=10\u2461
\u2460\u00d710-21\u00d7\u2461\uff0c\u53ef\u5f97
10y²-10x²-21xy=0
\u56e0\u5f0f\u5206\u89e3\uff0c\u5f97
(5y+2x)\u00d7(2y-5x)=0
\u6240\u4ee55y+2x=0\u2462
\u62162y-5x=0\u2463
\u5219\u53ef\u5316\u4e3a\u2462\u3001\u2460\u548c\u2463\u3001\u2460\u7684\u4e24\u4e2a\u540c\u89e3\u65b9\u7a0b\u7ec4
\u53735y+2x=0\u3001y²-x²=21\u62162y-5x=0\u3001y²-x²=21
\u7531\u2462\u53ef\u5f97x=-(5/2)\u00d7y\u2464
\u5c06\u2464\u4ee3\u5165\u2460\u5f97-(21/4)y²=0
\u6240\u4ee5y=0
\u4e0exy=10\u77db\u76fe
\u6240\u4ee5\u2462\u3001\u2460\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\u65e0\u89e3
\u7531\u2463\u53ef\u5f97x=(2/5)\u00d7y\u2465
\u5c06\u2465\u4ee3\u5165\u2460\u5f97(21/25)\u00d7y²=21
\u6240\u4ee5y=5\u6216-5
\u5c06y=5\u4ee3\u5165\u2465\u5f97x=2
\u5c06y=-5\u4ee3\u5165\u2465\u5f97x=-2
\u7efc\u4e0a\u53ef\u77e5\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a
x=2\uff0cy=5\u6216x=-2\uff0cy=-5
7.
x^2-2xy-y^2=1 , 2x^2-5xy-3y^2=0
2x^2-5xy-3y^2=0
(x-3y\uff09\uff082x+y\uff09=0
x=3y x= -0.5y
\u4ee3\u5165x^2-2xy-y^2=1\u4e2d\u89e3\u5f97y=\u00b1\u221a2/2 \uff1by=\u00b12
\u4ee3\u5165x=3y x= -0.5y\u4e2d\u89e3\u5f97x=\u00b13\u221a2/2\uff1bx=\u00b11
8.
x2+y2x2+y2+2xy=9
(x+y)²=9
x+y=3\u6216-3
(x-y)2-3x+3y+2=0
(x-y)²-3(x-y)+2=0
(x-y-1)(x-y-2)=0
x-y=1\u62162
\u6240\u4ee5\u7ec4\u62104\u4e2a\u65b9\u7a0b\u7ec4
x+y=3,x-y=1
x+y=3,x-y=2
x+y=-3,x-y=1
x+y=-3,x-y=2
\u6240\u4ee5
x=2,y=1
x=5/2,y=1/2
x=-1,y=2
x=-1/2,y=-5/2+2xy=9 (x-y)2-3x+3y+2=0
9.
x^2-y^2=6 (1)
2x^2+3y^2=72 (2)
\u7531(1)*2\u5f97\uff1a2x^2-2y^2=12 (3)
\u7531(2)-(3)\u5f97\uff1a5y^2=60 \u63a8\u5f97\uff1ay^2=12
\u7531\u6b64\u53ef\u5f97\uff1ax^2=18
\u6240\u4ee5\uff1ax=\u00b13\u500d\u6839\u53f72
y=\u00b12\u500d\u6839\u53f73
10.
x + 2y = 0 \uff081\uff09
x^2 + xy + y^2 + 5y = 0 \uff082\uff09
\u4e8c\u5143\u4e8c\u6b21\u65b9\u7a0b\u89e3\uff08\u8981\u8fc7\u7a0b\uff09
\u6d4f\u89c8\u6b21\u6570\uff1a18\u6b21\u60ac\u8d4f\u5206\uff1a5 | \u89e3\u51b3\u65f6\u95f4\uff1a2011-7-28 18:42 | \u63d0\u95ee\u8005\uff1a\u5c0f\u82b7\u828a
x + 2y = 0 \uff081\uff09
{
x^2 + xy + y^2 + 5y = 0 \uff082\uff09
\u6700\u4f73\u7b54\u6848 x=-2y
\u4ee3\u5165
4y²-2y²+y²+5y=0
y(3y+5)=0
y=0,y=-5/3
x=-2y
\u6240\u4ee5
x=0,y=0
x=10/3,y=-5/3
1) 66x+17y=3967
25x+y=1200
\u7b54\u6848\uff1ax=48 y=47
(2) 18x+23y=2303
74x-y=1998
\u7b54\u6848\uff1ax=27 y=79
(3) 44x+90y=7796
44x+y=3476
\u7b54\u6848\uff1ax=79 y=48
(4) 76x-66y=4082
30x-y=2940
\u7b54\u6848\uff1ax=98 y=51
(5) 67x+54y=8546
71x-y=5680
\u7b54\u6848\uff1ax=80 y=59
(6) 42x-95y=-1410
21x-y=1575
\u7b54\u6848\uff1ax=75 y=48
(7) 47x-40y=853
34x-y=2006
\u7b54\u6848\uff1ax=59 y=48
(8) 19x-32y=-1786
75x+y=4950
\u7b54\u6848\uff1ax=66 y=95
(9) 97x+24y=7202
58x-y=2900
\u7b54\u6848\uff1ax=50 y=98
(10) 42x+85y=6362
63x-y=1638
\u7b54\u6848\uff1ax=26 y=62
1\u30013x+70>100\u89e3:3x >100-70 3x>3O x>10
2\u30012x<x-3\u89e3: 2x-x<-3 x<-3
3\u30015-x4
4\u30012+2a>6\u89e3:2a>6-2 2a>4 a>2
5\u30012(x-2)>4\u89e3:2x-4>4 2x>4+4 2x>8 x>4
6\u300110-3(x+6)<1\u89e3:1O-3x-18<1 -3x<1-1O+18 -3x<9
7\u30016a+814
8\u30011/2-4.5 x<4.5
9\u30012x<1-4x\u89e3:2x+4x<1 6x<1 x<1/6
1O\u30013(y-2)+1<-2\u89e3:3y-6+1<-2 3y<-2+6-1 3y<3 y<1
{3x-8y=4②
由①得x=y+3③
③代入②得
3(y+3)-8y=4
y=1
所以x=4
则:这个二元一次方程组的解
{x=4
{y=1
2.{13x+14y=41 (1)
{14x+13y=40 (2)
解:(2)-(1)得
x-y=-1 即x=y-1 (3)
把(3)代入(1)得
13(y-1)+14y=41
所以13y-13+14y=41
27y=54 y=2
把y=2代入(3)得
即x=1
所以:x=1,y=2
3.(x+5)+(y-4)=8
(x+5)-(y-4)=4
令x+5=m,y-4=n
原方程可写为 m+n=8 m-n=4
解得m=6,n=2
所以x+5=6,y-4=2
所以x=1,y=6
4.x:y=1:4
5x+6y=29
令x=t,y=4t
方程2可写为:5t+24t=29 29t=29
t=1
所以x=1,y=4
5.x+y=5
3x+7y=-1
解:x=5-y
3(5-y)+7y=-1
15-3y+7y=-1
4y=-16
y=-4
得:x=9
6.解方程组x+y=5① 6x+13y=89②
解:由①得x=5-y③
把③带入②,得6(5-y)+13y=89,
解得y=59/7
把y=59/7带入③,
得x=5-59/7,即x=-24/7
∴x=-24/7,y=59/7
7.解方程组x+y=9① x-y=5②
解:①+②,得2x=14,
即x=7
把x=7带入①,得7+y=9,
解得y=2
∴x=7,y=2
8.22、王大伯承包了25亩土地,今年春季改种茄子和西红柿两种大棚蔬菜,用去了44000元。其中种茄子每亩用了1700元,获纯利2400元;种西红柿每亩用了1800元,获纯利2600元。问王大伯一共获纯利多少元?
解:设王大伯种了亩茄子,亩西红柿,根据题意得:
x+y=25
1700x+1800y=44000
解得:x=10
y=15
∴王大伯共获纯利:2400×10+2600×15=6300(元)
答:王大伯共获纯利6300元。
9.在社会实践活动中,某校甲、乙、丙三位同学一同调查了高峰时段北京的二环路、三环路、四环路的车流量(每小时通过观测点的汽车车辆数),三位同学汇报高峰时段的车流量情况如下:
甲同学说:“二环路车流量为每小时10000辆”
乙同学说:“四环路比三环路车流量每小时多2000辆”;
丙同学说:“三环路车流量的3倍与四环路车流量的差是二环路车流量的2倍”;
请你根据他们所提供的信息,求出高峰时段三环路、四环路的车流量各是多少?
设高峰时段三环路的车流量为每小时辆,四环路的车流量为每小时辆,根据题意得:
3x-y=22×10000 x=11000
解得
y=x+2000 y=13000
答:高峰时段三环路的车流量为每小时11000辆,四环路的车流量为每小时13000辆。
10.25、某同学在A、B两家超市发现他看中的随身听的单价相同,书包单价也相同,随身听和书包单价之和是452元,且随身听的单价比书包单价的4倍少8元。
求该同学看中的随身听和书包单价各是多少元?
设书包的单价为元,随身听的单价为元
x+y=425
根据题意,得
y=4x-8
解这个方程组,得 x=92
y=360
答:该同学看中的随身听单价为360元,书包单价为92元。
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