It is known that for any rational number a and B, the binary linear equation (a-b) x - (a + b) y = a + B with respect to X and y has a set of common solutions, then the common solution is___ ．

It is known that for any rational number a and B, the binary linear equation (a-b) x - (a + b) y = a + B with respect to X and y has a set of common solutions, then the common solution is___ ．

It is known that a (x-y-1) - B (x + y + 1) = 0, i.e. x-y-1 = 0, ① x + y + 1 = 0, ②, ① + ②, 2x = 0, x = 0; substituting x = 0 into ①, y = - 1, so the solution of this equation system is: x = 0y = - 1. So the answer is: x = 0y = - 1 For any rational number a, B, the binary linear equation (a-b) x - (a + b) y = a + B has a set of common solutions, so let a = 1, B = - 1 (a + B = 0), then (a-b) x - (a + b) y = a + B is: 2x = 0, x = 0, let a = b = 1, (a-b = 0), then (a-b) x - (a + b) y = a + B is: - 2Y = 2, y = - 1, so the common solution is: x = 0, y = - 1

At the beginning of the new semester, in order to enhance the cohesion of the group, the group leader asked the whole group to send one card to each other. It is known that the whole group sent 132 cards. How many people are there in the group?

The answer downstairs is correct
I'd like to explain here: because it's sending cards to each other, there are x people, each of whom has to send (x-1) cards (because he doesn't have to send them to himself), so x people have to send x (x-1) cards, that is 132 cards
So the equation listed is x (x-1) = 132

Mathematical problems, on the use of binary linear equation
In the NBA regular season, Yao Ming, a famous basketball player in China, scored 22 points in 14 of 22 shots in a game. If he made two three-point shots, he also made several two-point shots and several free throws (1 point in one free throw)

Hit x two pointers and Y free throws
3*2+x*2+y=22
2+x+y=14
x=4 y=8

How to do this math problem with quadratic equation
For a rectangle, the length is reduced by 20 and the width is increased by 15 to get a square whose area is equal to that of the rectangle

Let the length of the original rectangle be C and the width be K~
Then: (C-20) = (K + 15)
(C-20)(K+15)=CK
Simplification: c-k = 35
15C-20K=0
C, K can be obtained from the solution

Two mathematical problems, with a binary equation to do（
(1) A class participated in the activity, some students carried the soil, and some students carried the soil. It is known that the whole class shared 59 soil baskets and 36 shoulder poles. How many people are there in total?
(2) In the flood season, the students of class 1, Grade 7 went to the reservoir to investigate the data. There are 10 flood sluices in the reservoir. Now the water level of the reservoir exceeds the safety line, and the upstream river still flows into the reservoir like a constant flow rate. After one day's investigation, the students made the following records: open a flood sluice in the morning, the water level continues to rise by 0.66M within 2 hours, and open two flood sluices in the afternoon, Within 4 hours, the water level dropped by 0.1M, and the current water level is still 1.2m above the safety line
1. If five floodgates are opened, how many hours will it take to reach the safety line?
2. If the flood control headquarters requires the water level to be lowered to the safety line within 6 hours, how many floodgates should be opened?

If there are x soil lifters and Y soil lifters, then x / 2 + 2Y = 59x / 2 + y = 36, and the solution is x = 26, y = 23. Answer: there are 49 soil lifters and Y soil lifters in total. If the flow velocity into the reservoir is x m / h, and the flow velocity of a sluice is Y M / h, then 2x-2y = 0.668y-4x = 0.1, and the solution is x = 0.685