In this paper, we study the solution of the following system of linear equations of two variables （1)2X-Y=1 2X+Y=1 （2）2X-Y=1 4X-2Y=1 （3）2X-Y=1 6X-3Y=3 Conjecture induction: for binary linear equations, a1x + b1y = C1, a2x + a2y = C2 (A1, A2, C1, C2 are not zero), 1. There is a unique solution for river time? 2.3. When there are innumerable solutions? 4. Don't understand the equations and judge the solution of the equations y = KX + b y = (3K-1) x + 2 about X and y

(1) There are unique solutions, (2) no solutions, (3) numerous solutions. Induction: for a1x + b1y = C1, a2x + a2y = C2 (A1, A2, C1, C2 are not 0), when A1: A2 is not equal to B1: B2, the equations have unique solutions; when A1: A2 = B1: B2 is not equal to C1: C2, there are no solutions. When A1: A2 = B1: B2 = C1: C2, there are numerous solutions

A person saves 3000 yuan in two forms. The first is current deposit with an annual interest rate of 0.98%, and the second is one-year fixed deposit with an annual interest rate of 1.98%. To make the total interest after one year equal to 1.2% of the principal, how many yuan should these two kinds of deposits be deposited

x+y=3000
0.98%*x+1.98%*y=1.2%*3000

When someone goes along the highway at a constant speed, he meets a bus coming in front of him every 4 minutes, and a bus overtakes him from behind every 6 minutes. Assuming that the speed of the car remains the same, and the distance between two adjacent cars coming in front of him and the distance between two adjacent cars coming from behind is 1200m, find out the speed of someone and the speed of the bus, and the car leaves one every few minutes?

Suppose that the speed of a person is am / min and the speed of a bus is XM / min. from the question meaning: 4A + 4x = 12006x − 6A = 1200, the solution is: a = 50x = 250, then the departure time of a car every few minutes is = 1200 △ 250 = 4.8 (min). Answer: the speed of a person is 50M / min, the speed of a bus is 250m / min, and the bus leaves every 4.8min

Factorization: 2 (a ^ 2-3mn) + a (4m-3n)

2(a^2-3mn)+a(4m-3n)
=2a^2-6mn+a(4m-3n)
=2a^2+a(4m-3n)-6mn
=(2a-3n)(a+2m)

The ratio of zero two to zero four

It's 2-4

The solution of the square of x-16x = 100

（8±2√41）
(2 √ 41) denotes 41 under the root of 2

4X/5x—2+5x—2/4x=17/4

Let a = 4x / (5x-2)
Then (5x-2_ )/4x=1/a
a+1/a=17/4
Take 4A on both sides
4a²-17a+4=0
(4a-1)(a-4)=0
a=1/4,a=4
4x/(5x-2)=1/4
5x-2=16x
x=-2/11
4x/(5x-2)=4
5x-2=x
x=1/2
So x = - 2 / 11, x = 1 / 2

If M + n = 2, then the value of m2-n2 + 4N is______ ．

∵ m + n = 2, ∵ original formula = (M + n) (m-n) + 4N = 2 (m-n) + 4N = 2m-2n + 4N = 2 (M + n) = 2 × 2 = 4

2008 + 200.8 + 20.08 + 2.008 + 1992 + 199.2 + 19.92 + 1.992?

The original formula = 2008 + (200.8 + 199.2) + (20.08 + 19.92) + (2.008 + 1.992) (using the law of association)
=2008+400+40+4
=2452

The perimeter of a right triangle is 36 cm, and the length ratio of the three sides is 3:4:5. How many square centimeters is the area of the triangle?

36 × 33 + 4 + 5 = 9 (CM), 36 × 43 + 4 + 5 = 12 (CM), 9 × 12 △ 2 = 54 (square cm). A: the area of this triangle is 54 square cm