二元一次方程知识点总结加经典习题

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1、二元一次方程组知识点1、 二元一次方程的定义：含有两个未知数，并且未知数的项的次数都是1，像这样的方程叫做二元一次方程。2、 二元一次方程组的定义：把具有相同未知数的两个二元一次方程合在一起，就组成了一个二元一次方程组。3、 二元一次方程组的解：一般地，使二元一次方程两边的值相等的两个未知数的值，叫做二元一次方程的解，二元一次方程有无数个解。4、 二元一次方程组的解：一般地，二元一次方程组的两个方程的公共解，叫做二元一次方程组的解。5、 代入消元法解二元一次方程组：（1） 基本思路：未知数又多变少。（2） 消元法的基本方法：将二元一次方程组转化为一元一次方程。（3） 代入消元法：把二元一次方程

2、组中一个方程的未知数用含另一个未知数的式子表示出来，再代入另一个方程，实现消元，进而求得这个二元一次方程组的解。这个方法叫做代入消元法，简称代入法。（4） 代入法解二元一次方程组的一般步骤：1、 从方程组中选出一个系数比较简单的方程，将这个方程中的一个未知数（例如y）用含另一个未知数（例如x）的代数式表示出来，即写成y=ax+b的形式，即“变”2、 将y=ax+b代入到另一个方程中，消去y，得到一个关于x的一元一次方程，即“代”。3、 解出这个一元一次方程，求出x的值，即“解”。4、 把求得的x值代入y=ax+b中求出y的值，即“回代”5、 把x、y的值用联立起来即“联”6、 加减消元法解二元

3、一次方程组（1） 两个二元一次方程中同一个未知数的系数相反或相等时，把这两个方程的两边分别相加或相减，就能消去这个未知数，得到一个一元一次方程，这种方法叫做加减消元法，简称加减法。（2） 用加减消元法解二元一次方程组的解1、 方程组的两个方程中，如果同一个未知数的系数既不互为相反数幼不相等，那么就用适当的数乘方程两边，使同一个未知数的系数互为相反数或相等，即“乘”。2、 把两个方程的两边分别相加或相减，消去一个未知数、得到一个一元一次方程，即“加减”。3、 解这个一元一次方程，求得一个未煮熟的值，即“解”。4、 将这个求得的未知数的值代入原方程组中任意一个方程中，求出另一个未知数的值即“回代”

4、。5、 把求得的两个未知数的值用联立起来，即“联”。1在方程中，如果用含有的式子表示，则 2下列方程中，那些是二元一次方程？ （1） (2) (3) (4) (5)3已知方程2x2m+3+3y4n-7=4是关于x、y的二元一次方程，则m为多少？4方程（k2-4）x2+(k+2)x+(k-6)y=k+8是关于x、y的方程，则：当k为何值时，方程为一元一次方程？当k为何值时，方程为二元一次方程？5请写出一个以为解的二元一次方程组 6（1） （2）（3） （4） 7已知是方程组的解，求的值。8已知等式，当时，；当时，；求的值9方程组的解为则被遮盖的两个数分别为多少？10若方程组的解x和y的和为0，求

5、k的值。11已知方程组的解适合方程，求m的值12已知方程组与方程组的解相同，求a,b的值13若方程组与方程组有相同的解，求a，b的值。14小红和小丽共同解方程组，由于小红看错了a的值，求得的解是，小丽看错了b的值，求得的解是，（1）你能求出a，b的正确的值吗？（2）方程组的正确的解为多少？15若，则的值为多少？二元一次方程组应用题1、 一、列二元一次方程组解应用题的一般步骤可概括为“审、找、列、解、答”五步，即：2、 审：通过审题，把实际问题抽象成数学问题，分析已知数和未知数，并用字母表示其中的两个未知数；3、 找：找出能够表示题意两个相等关系；4、 列：根据这两个相等关系列出必需的代数式，从

6、而列出方程组；5、 解：解这个方程组，求出两个未知数的值；6、 答：在对求出的方程的解做出是否合理判断的基础上，写出答案二、典型例题讲解题型一、列二元一次方程组解决生产中的配套问题1、 某服装厂生产一批某种款式的秋装，已知每2米的某种布料可做上衣的衣身3个或衣袖5只，贤计划用132米这样布料生产这批秋装（不考虑布料的损耗），应分别用多少布料才能使做的衣身和衣袖恰好配套题型二、列二元一次方程组解决行程问题2、 甲、乙两地相距160千米，一辆汽车和一辆拖拉机同时由甲、乙两地相向而行，1小时20分相遇。相遇后，拖拉机继续前进，汽车在相遇处停留1小时候后调转车头原速返回，在汽车再次出发后半小时后追上乐

7、拖拉机，这时，汽车、拖拉机各行驶了多少千米？3、 一轮船从甲地到乙地顺流航行需4小时，从乙地到甲地逆流航行需6小时，那么一木筏由甲地漂流到乙地需要多长时间？题型三、列二元一次方程解决商品问题4、 在“五一”期间，某超市打折促销，已知A商品7.5折销售，B商品8折销售，买20件A商品与10件B商品，打折前比打折后多花460元，打折后买10件A商品和10件B商品共用1090元。求A、B商品打折前的价格。题型四、列二元一次方程组解决工程问题5、 某城市为了缓解缺水状况，实施了一项饮水工程，就是把200千米以外的一条大河的水引到城市中来，把这个工程交给甲、乙两个施工队，工期为50天，甲、乙两队合作了3

8、0天后，乙队 因另外有任务需要离开10天，于是甲队加快速度，每天多修0.6千米，10天后乙队回来后，为了保证工期，甲队保持现在的速度不变，乙队每天比原来多修0.4千米，结果如期完成，问：甲、乙两队原计划每天各修多少千米？题型五：列二元一次方程组解决增长问题6、 某中学现有学生4200人，计划一年后初中在校学生增加8%，高中在校学生增加11%，这样全校在校生将增加10%，则该校现在有初中生多少人？在校高中生有多少人？English is the most widely spoken language in the history of our planet, used in some way b

9、y at least one out of every seven human beings around the globe. Half of the worlds books are written in English, and the majority of international telephone calls are made in English. English is the language of over sixty percent of the worlds radio programs. More than seventy percent of internatio

10、nal mail is written and addressed in English, and eighty percent of all computer text is stored in English. English has acquired the largest vocabulary of all the worlds languages, perhaps as many as two million words, and has generated one of the noblest bodies of literature in the annals of the hu

11、man it is now time to face the fact that English is a crazy language - the most lunatic and loopy and of all languages. In the crazy English language, the blackbird hen is brown, blackboards can be green or blue, and blackberries are green and then red before they are ripe. Even if blackberries were

12、 really black and blueberries really blue, what are strawberries, cranberries, huckleberries, raspberries, and gooseberries supposed to look add to this insanity there is no butter in buttermilk, no egg in eggplant, no grape in grapefruit, no bread in shortbread, neither worms nor wood in wormwood,

13、neither mush nor room in mushroom, neither pine nor apple in pineapple, neither peas nor nuts in peanuts, and no ham in a hamburger. (In fact, if somebody invented a sandwich consisting of a ham patty in a bun, we would have a hard time finding a name for it.)To make matters worse, English muffins w

14、erent invented in England, fries in France, or Danish pastries in Denmark. And we discover even more culinary madness in the that sweetmeat is made from fruit, while sweetbread, which isnt sweet, is made from this unreliable English tongue, greyhounds arent always grey (or gray); panda bears and koa

15、la bears arent bears (theyre marsupials); a woodchuck is a groundhog, which is not a hog; a horned toad is a lizard; glowworms are fireflies, but fireflies are not flies (theyre beetles); ladybugs and lightning bugs are also beetles (and to, a significant proportion of ladybugs must be male); a guin

16、ea pig is neither a pig nor from Guinea (its a South American rodent); and a titmouse is neither is like the air we breathe. Its invisible, inescapable, indispensable, and we take it for granted. But, when we take the time to step back and listen to the sounds that escape from the holes in peoples f

17、aces and to ex- the paradoxes and vagaries of English, we find that hot dogs can be cold, darkrooms can be lit, homework can be done in school, nightmares can take place in broad daylight while morning sickness and daydreaming can take place at night, tomboys are girls and midwives can be men, hours

18、 - especially happy hours and rush hours - often last longer than sixty minutes, quick- sand works very slowly, boxing rings are square, silverware and glasses can be made of plastic and tablecloths of paper, most are dialed by being punched (or pushed?), and most bathrooms dont have any baths in th

19、em. In fact, a dog can go to the bathroom under a tree - no bath, no room; its still going to the bathroom. And doesnt it seem a little bizarre that we go to the bathroom in order to go to the is it that a woman can man a station but as man cant woman one, that a man can father a movement but a woma

20、n cant mother one, and that a king rules a kingdom but a queen doesnt rule a? How did all those Renaissance men reproduce when there dont seem to have been any Renaissance writer is someone who writes, and a stinger is something that stings. But fingers dont grocers dont, haberdashers dont, hammers

21、dont ham, and humdingers dont the plural of tooth is teeth , shouldnt the plural of booth be ? One goose, two geese - so one moose, two One index, two indices - one Kleenex, two If people ring a bell today and rang a bell yesterday, why dont we say that they a ball? If they wrote a letter, perhaps t

22、hey also their tongue. If the teacher taught, why isnt it also true that the preacher? Why is it that the sun shone yesterday while I shined my shoes, that I treaded water and then trod on the beach, and that I flew out to see a World Series game in which my favorite player flied we conceive a conce

23、ption and receive at a reception, why dont we grieve a and believe a? If a horsehair mat is made from the hair of horses and a camels hair brush from the hair of camels, from what is a mohair coat made? If adults commit adultery, do infants commit infantry? If olive oil is made from olives, what do

24、they make baby oil from? If a vegetarian eats vegetables, what does a humanitarian eat? (And Im beginning to worry about those authoritarians.)And if pro and con are opposites, is congress the opposite of you have to believe that all English speakers should be committed to an asylum for the verbally

25、 insane. In what other language do people drive in a parkway and park in a driveway? In what other language do people recite at a play and play at a recital? In what other language do privates eat in the general mess and generals eat in the private mess? In what other language do people ship by truc

26、k and send cargo by ship? In what other language can your nose run and your feet can a slim chance and a fat chance be the same and a bad licking and a good licking be the same, while a wise man and a wise guy are opposites? How can sharp speech and blunt speech be the same and quite a lot and quite

27、 a few the same, while overlook and oversee are opposites? How can the weather be hot as hell one day and cold as hell the next? How can the expressions Whats going on? and Whats coming off? mean exactly the samton and unbutton and tie and untie are opposites, why are loosen and unloosen and ravel a

28、nd unravel he same? If bad is the opposite of good, hard the opposite of soft, and up the opposite of down, why are badly and goodly, hardly and softy, and upright and downright not opposing pairs? If harmless actions are the opposite of harmful why are shameful and shameless behavior the same and p

29、ricey objects less expensive than priceless appropriate and inappropriate remarks and passable and impassable mountain trails are opposites, why are flammable and inflammable materials, heritable and inheritable property, and passive and impassive people the same and valuable objects less treasured

30、than invaluable ones? If uplift is the same as lift up, why are upset and set up opposite in meaning? Why are pertinent and impertinent, canny and uncanny, and famous and infamous neither opposites nor the same? How can raise and raze and reckless and be opposites when each pair contains the same is

31、 it that when the sun or the moon or the stars are out, they are visible, but when the lights are out, they are invisible; that when I clip a coupon from a newspaper I separate it, but when I clip a coupon to a newspaper, I fasten it; and that when I wind up my watch, I start it, but when I wind up

32、this essay, I shall end is a crazy can expressions like Im mad about my flat, No football coaches allowed, Ill come by in the morning and knock you up, and Keep your pecker up convey such different messages in two countries that purport to speak the same can it be easier to assent than to dissent bu

33、t harder to ascend than to descend? Why it is that a man with hair on his head has more hair than a man with hairs on his head; that if you decide to be bad forever, you choose to be bad for good; and that if you choose to wear only your left shoe, then your left one is right and your right one is left? Right?