Find a few problems with binary equations in ancient mathematics

1.There is a question of "chickens and rabbits in the same cage" in the ancient mathematical work "Sun Tzu's Sutra": "Today there are chickens and rabbits in the same cage, with thirty-five heads on the top and ninety-four feet on the bottom. ”

2.There is such a question in the world-famous arithmetic book "Nine Chapters of Arithmetic": "Today, there are good deeds who do 100 steps, and those who do not do good deeds take 60 steps.

Meaning: When a fast walker walks 100 steps, a slow walker walks only 60 steps A slow walker walks 100 steps first, and how many steps does a fast walker have to take to catch up?

3.Another famous title in "Sun Tzu's Sutra": "There is wood today, I don't know the length of the rope, the remaining rope is four feet five inches, the rope is bent, less than one foot, how long is the wood?"

Meaning: Use a rope to measure a long log, the rope still has a ruler, fold the rope in half and measure the long wood, the long wood is still 1 foot, ask how long the wood is long?

4.Cheng Dawei, a famous mathematician in the Ming Dynasty, wrote such a question: "100 monks are divided into 100 steamed buns, the big monks eat 3 each, and the small monks eat 1 for every 3 people, and ask the big and small monks how much".

5.The famous mathematical problem circulated among the people in my country: I only heard that the person next door divided the silver, and I don't know how much silver and people; 7 taels per person, 7 taels less, half a catty per person, more than half a catty; Let me ask you good calculators, how many people share how much silver? (Note: Jin here refers to the city catty, 1 city jin = 10 taels).

1.Big cart x small car y

12x+5y=99

There's nothing you can do about it

You'll have to try them one by one

x=0

However, the mantissa of 99 is 9....The mantissa of the number of people in the car is either 5 or 05, and the mantissa of the number of people in the car must be 4, and it is impossible to x=2 y=15 when the same 0

x=7 y=3

2（x-y)-5(x+y)=-1

3x - 7y=-1 ②②3①

32y=-64

y=-2x=5

1.There are two schemes: let the big car have x cars, the small car has y cars, and the equation is 12x+5y=99, and x and y must be integers, so the solution is (1).2 large cars, 15 small cars; (2) 7 large cars and 3 small cars.

2.Is the following equation 2(x-y)-5(x+y)=-1? The steps to solve this problem are:

6x-6y-7x-7y=21┈┈┈x-13y=21

2x-2y-5x-5y=-1┈┈┈3x-7y=-1

Simultaneous solution of the above two equations gives x=-2 and y=1

3.The system of simultaneous equations 5x+y=3 x-2y=5 is solved to obtain x=1, y=-2Substituting the values of x and y into the equations ax+5y=8 and 5x+by=1 gives the new equation a-10=8,5-2b=1, which results in a=18,b=2

4.Is the title correct???

5.Solving the equation 2x+y=3 x+y=1 gives x=2, y=-1Substituting the values of x and y into ax+2y=4-a to get 2a-2=4-a to get a=2

Let the ten-digit number be vertical defeat and the single-digit number be .

10 early to do 5 15

Just put these two equations together and make a system of equations and solve them.

Hopefully, you can understand that I wish you better and better grades.

Solution: Set up x tickets for type A and Y tickets for type B.

Then there is an equation: x+y=35 (a total of 35 students) 24x+18y=750 (a total of 750 yuan).

Solve x=20, y=15

A: I bought 20 tickets for type A and 15 tickets for type B.

Let A x and B y , then x+y=3=5 24x+18y=750 to obtain x=20 y=15

Let the walking speed be x meters per day, and the speed of the fire model is y meters per second. Extinction.

Then 15x+15y=255, 17y-17x=225 solve this system of equations, and get x=1, y=16

Answer: People: 1 Train: 16

x--5y=9 (1)

x--2y=6 (2)

1)--2) got.

3y=--3

y=--1 substitute y=--1 into (2).

x+2=6x=4 So the solution of the original equation is: x=4, y=--1

5m--2n=11 (1)

2m--3n=--11 (2)

1)*3--(2)*2

11m=55

m=5 is obtained by substituting m=5 into (1).

25--2n=11

2n=--14

n=7.So the solution of the original equation is: m=5, n=7

x+y=80 (1)

x+2y=60 (2)

2)--1) Got.

y=--20

Substituting y=--20 into (1) obtains.

x--20=80

x=100.

So the solution of the original equation is: x=100, y=--20

2x--15y=550 (1)

10x+3y=6800 (2）

2)--1)*5 Get.

78y=4050

y=675/13

Substituting y=675 13 into (1) yields.

2x--11125/13=550

2x=18275/13

x=18275/26

So the solution of the original equation is: x=18275 26, y=675 13

Untie. According to the title, it can be seen that team A can complete 1 12 of the project every day, team B can complete 1 15 of the project every day, and C can complete 1 20 of the project every day.

y=(7-1-x)=(6-x)

1 12 + 1 15) * x + (1 12 + 1 15 + 1 20) * y = 1 substitute y into .

1/12+1/15)*x+(1/12+1/15+1/20)*(6-x)=1

Multiply both sides of the equation by 60 to get.

5+4)x+(5+4+3)(6-x)=60 The solution gives x=4y=6-4=2

So teams A and B worked together for 4 days, and team C did it for another 2 days after they joined.

Substituting x=1, y=-1, and x=2, y=3 into the equation y=kx+b, respectively, gives equations (1)-1=k+b, and equations (2)3=2k+b; Using the system of equations to solve, (2)-(1) obtains k=4, and then substituting k=4 into equation (1) obtains -1=4+b; Obviously, b=-5, so the equation is y=4x-5,.

Substituting x=1,y=-1 and x=2,y=3 into the equation y=kx+b has: -1=k+b

3=2k+b

Solution: k=4, b=-5 Substituting it into the equation y=kx+b gives the equation: y=4x-5