Questions about binary equations Optimization Training .

x+1641y=28359

1641x+8359y=21641

Add x+y=5

Subtract x-y=1 to get x=3 y=1

2、x+1／

The whole understanding is x=5 4 y=5 12

x-2／y=3

2／x+3／y=-1

Multiply the above equation by 2 and subtract the lower formula to get y=-1 x=1

x/3+y/4=4/3

4(x+2)=3(y-4)

2/3)x+(5/6)y=1

1/3)x+(1/6)y=-1

1. It becomes 4x+3y=16 4x-3y=-20x= y=6

2. Add x+y=0

Bring in the solution to get x=-6 y=6

x-3/3=y+6/5

14x+3y=24

x-1=y+ x-y= 3x-3y=

x= y=3x+y=34

8x+3y=30

7x+4y=62

9x+2y=87

2x+5y=19

3x+5y=56

5x+2y=22

7x+7y=203

x+4y=21

5x+8y=44

3x+4y=38

4x+y=29

9x+5y=46

4x+3y=36

7x+4y=42

4x+y=41

x+6y=27

4x+7y=95

3x+6y=18

7x+9y=69

7x+8y=62

3x+3y=27

2x+8y=26

7x+6y=74

4x+6y=16

6x+3y=42

7x+y=11

8x+6y=94

7x+6y=66

7x+2y=47

Find the integer solution of the indefinite equation system 5x+9y=104.

Solution: 5x+9y=104

x=104-9y/5

Because x and y are natural numbers, 104-9y is a multiple of 5.

When y is 1, 6, 11, the corresponding x can be 19, 10, 1

So the solution of the equation is (x=19 y=1), (x=10, y=6) (x=1, y=11).

Xiaoliang speed x, Xiaoying quick rent Kantar y

5x=5y+10

4x=（2+4）y

Solving this equation is the type of perturbation.

x=6，y=4

1 Among the following equations, the binary equation is ( ).

a．3x－2y=4z b．6xy+9=0 c． +4y=6 d．4x=

2 In the following system of equations, the system of binary linear equations is ( ).

a 3 binary linear equation 5a 11b = 21 (

A has one and only one solution b has an infinite number of solutions c has no solution state d has and only two solutions.

4 The common solution of the equation y=1 x and 3x+2y=5 is ( ).

a 5 If x 2 +(3y+2)2=0, then the value is ( ).

a．－1 b．－2 c．－3 d．

6. The solution of the equation is , then a, b are ( ).

a、 b、 c、 d、

7、|3a＋b＋5|＋|2a－2b－2|0, then the value of 2a2 3ab is ( ).

a、14 b、2 c、－2 d、－4

8. When solving the system of virtual oak equations, the simpler method is ( ).

A, substitution method B, addition and subtraction C, test value method D, can not be determined.

9. A store has two headphones with different prices that are sold for 64 yuan, one of which makes a profit of 60% and the other loses 20%.

a, lose 8 yuan b, earn 32 yuan c, do not lose do not earn d, earn 8 yuan.

2. Fill in the blanks.

1 The known equation 2x+3y 4=0 is expressed by the algebraic expression of y with x: y= The algebraic expression of x with y is: x=

2 In the binary linear equation x+3y=2, when x=4, y= when y= 1, x=

3 If x3m 3 2yn 1=5 is a binary equation, then m= n=

4 is known to be the solution of the equation x ky=1, then k=

5 Knowing x 1 +(2y+1)2=0, and 2x ky=4, then k=

6 The positive integer solution of the binary linear equation x+y=5 has

7 A binary linear equation with a solution of is

9. The first batch of goods totaling 480 tons was loaded with 8 train cars and 20 cars; The second batch transported a total of 524 tons, with 10 train cars and 6 cars exactly loaded, how many tons of each train car and each car were loaded on average?

10. One Thousand and One Nights There is a passage in which there is a flock of pigeons, some of which are singing in the trees and the other foraging on the ground, and one of the pigeons in the trees says to the doves foraging on the ground: "If one flies up from among you, the doves under the tree belong to the whole flock, and if one flies down from the tree, there are as many pigeons on the tree and under the tree."

Do you know how many pigeons there are in the tree and under the tree? Agree.

There are 60 monks who eat 60 steamed buns, if the big monk eats 3 per person, and the small monk eats one for every 3 people, then the big monk has it? Person.

As the question: 2x+3y=8

3x+2y=7

The simplest way is the fundamental identity relation, where the addition or subtraction of both sides of the = sign is still equal, and x+y=3 can be obtained, i.e., x=3-y

Contribute (3-y) to any one of the agendas, and you can get x, that is, y.

Basically, it's about using identity, or using one equation to find x or y and bring in another equation to solve.

Simple enough.

Application questions of one-dimensional quadratic equations (intermediate school examination questions).

Growth Rate Question:

1. (Dalian, 2003) After several years of unremitting efforts, a housing development company has developed and constructed a residential area from 40,000 square meters in 2000 to 70,000 square meters in 2002. Suppose the average annual growth rate of the residential area developed and constructed by the housing development company in these two years is x, then the equation can be as follows

2. (2003 Beijing Xicheng) Hongxin Machinery Factory produces a certain type of blower, and the output from January to June is as follows:

Months 1 2 3 4 5 6.

Production (sets) 50 51 48 50 52 49(1) Find the monthly output of the blower in the first half of the year, the average and the median;

2) Due to the improvement of production technology, it is planned to produce 72 blowers in August, what is the average monthly growth rate of blower production in July and August compared to the average monthly output in the first half of the year?

A system of binary linear equations.

1.If is a binary equation, then ( )a b. c. d.

2.There are ( ) positive integer solutions to a binary linear equation. a. 1 b. 2 c. 3 d. 4

3.There is a two-digit number, and the sum of its ten digits and the single digit number is 6, and the number of such two digits has ( ).

a. 3 b. 5 c. 6 d.Countless.

4.Known , then b 4 c. 6 d. 7

5. If the solution of the system of equations satisfies 0, then the range of values for is ( ).

a、 ＜1 b、 ＜1 c、 ＞1 d、 ＞1

6.Knowing that the system of equations has the same solution as , then

7.If there is a common solution to a binary equation , then the value of is ( ).

a、3 b、－3 c、－4 d、4

8. If , the value of is .

9. Knowing that the algebraic formula and are the same kind of terms, then the values of are ( ).

a． b． c． d．

10.If the solution of the binary linear simultaneous equation is x=a,y=b, then a b=? （

a) (b) (c) (d) 

11. When solving a system of equations, a student misreads and obtains , and the correct solution is then , the value of , is ( ).

12.A square table consists of 1 table top and 4 legs. If 1 cubic meter of wood can be used to make 50 tabletops or 300 table legs, and there are 10 cubic meters of wood, then how many cubic meters of wood can be used to make a tabletop, how many cubic meters of wood can be used to make table legs, and the table top and table legs can be made just to match a square table?