X ^ 2 + y ^ 2 + 2x + 8y-8 = 0 and x ^ 2 + y ^ 2-4x-4y-2 = 0

X ^ 2 + y ^ 2 + 2x + 8y-8 = 0 and x ^ 2 + y ^ 2-4x-4y-2 = 0

Xinyue Xinchi: X & sup2; + Y & sup2; + 2x + 8y-8 = 0x & sup2; + Y & sup2; - 4x-4y-2 = 0, that is: X & sup2; + Y & sup2; + 2x + 8y = 8, ① X & sup2; + Y & sup2; - 4x-4y = 2, ② ① - ②, 12Y + 6x = 62y + x = 1x = 1-2y, ③ substitute ③ into ①, get (1-2y) & sup2; + Y & sup2; + 2 (1-2y) + 8y = 81 + 4Y &
Find the solution of {5x-3y + Z = - 2, 5x + 2y-4x = 3, - 5x + Y-Z = 2} equations
From 1 + 2, we get
Namely
Get 2 + 3
Substituting XX = XX into 1, we get
Substituting XX = XX, XX = XX into 1, we get
So, the solution of the original equation is
From 1-2, 5z-5y = - 5
That is Z-Y = - 1
From 1 = 3, - 2Y = 0
The solution is y = 0
Substituting y = 0 into Z-Y = - 1, we get z = - 1
Substituting y = 0, z = - 1 into {5x-3y + Z = - 2, we get
The solution is x = - 1 / 5
So the solution of the original equation is x = - 1 / 5, y = 0, z = - 1
From 1-2, we get
That is 5z-3y = - 5
From 2 + 3, we get
The solution is 3y-5z = 5
One of the three equations is wasteful, that is, the third one can be deduced from two equations
So, the equation has innumerable solutions.
Find the solution of {5x-3y + Z = - 2, 5x + 2y-4z = 3, - 5x + Y-Z = 2} equations
From 1 + 3 we get - 2Y = 0, that is y = 0
From 2 + 3 we get - 5Z = 5, that is Z = - 1
Substituting 1 gives 5x = - 1; that is, x = - 1 / 5.
x=50/4 y=-19/4 z=-115/4
Circle C1: X & # 178; + Y & # 178; + 2x + 8y-8 = 0 circle C2: X & # 178; + Y & # 178; - 4x-4y-2 = 0
Circle C1: X & # 178; + Y & # 178; + 2x + 8y-8 = 0 circle C2: X & # 178; + Y & # 178; - 4x-4y-2 = 0
What are the coordinates of the two intersections of? They are (3, - 1) and (- 1,
Circle C1: X & # 178; + Y & # 178; + 2x + 8y-8 = 0 circle C2: X & # 178; + Y & # 178; - 4x-4y-2 = 0
Subtraction
6x+12y-6=0
x+2y-1=0
After inspection
(3, - 1) on a straight line, and on a circle, so
yes.
But (- 1, - 7) is not
(- 1, - 1) yes
Their intersection chord is x + 2y-1 = 0, which is associated with the circle, one (3, - 1), one (- 1,1)
I brought it in for you,
(3, - 1) yes
(- 1, - 7) No
The method is to satisfy two analytic expressions. Do you have any questions? Thank you
The most important thing is to understand the method. Good luck
（-1，1）（3，-1）
Solve the equations 2x + 3Y = 5, - 5x-7y = 1
2x+3y=5
14x+21y=15
-5x-7y=1
-15x-21y=3
Two formula addition
14x-15x=15+3
-x=18
x=-18
3y=5-2x=5+2x18
3y=41
y=41/3
If you don't understand this question, you can ask,
2x+3y=5
14x+21y=15
-5x-7y=1
-15x-21y=3
Two formula addition
14x-15x=15+3
-x=18
x=-18
3y=5-2x=5+2x18
3y=41
y=41/3
Hope to adopt
Given circle C1: X & # 178; + Y & # 178; + 2x + 8y-8 = 0, circle C2: X & # 178; + Y & # 178; - 4x-4y-2 = 0. Find the linear equation and common chord length of two circles
How to solve the equations 2x-3y = 8 5x-7y = 5
2x-3y=8 ①
5x-7y=5 ②
① 10x-15y = 40 for * 5
② * 2 is 10x-14y = 10 ④
④ - y = - 30
Take y = - 30 into ① to get
x=-41
2x-3y=8 5x-7y=5
7x(2x-3y)=8x7=56 14x-21y=56
3x(5x-7y)=5x3=15 15x-21y=15
By subtracting the upper and lower expressions, X can be solved, and then by bringing x into the original expression, y can be solved
2x-3y = 8 times 5 leads to 10x-15y = 40
5x-7y = 5 times 2 leads to 10x-14y = 10
Subtract to get - y = 30 ∥ y = - 30
Substitute y = - 30 to get x-41
The square of 2Y + 4Y = 5
The square of 2Y = 5Y
The square of Y + 2Y = 5 / 2
y²+2y+1=7/2
(y+1)²=7/2
y+1=±√14/2
y=-1±√14/2
Solving the equations {1 / 5x + 1 / 3Y = 2 / 50.5x-0.3y = 0.2
The solution of {1 / 5x + 1 / 3Y = 2 / 5,0.5x-0.3y = 0.2 is obtained by addition and subtraction method
Please check whether it is the correct answer, thank you
Sort it out first
1/5x+1/3y=2/5
Take 15 on both sides
3x+5y=6 (1)
0.5x-0.3y=0.2
Take 10 on both sides
5x-3y=2 (2)
(1)×3+(2)×5
9x+15y+25x-15y=18+10
34x=28
x=14/17
y=(5x-2)/3=12/17
The second equation is multiplied by 2 to get x-0.6y = 0.4
Multiply the first equation by 5 to get x + 5 / 3Y = 2
I want to reduce it
y=12/17,x=14/17
Results brought in
Multiply the first equation by 5 to get x + 5 / 3Y = 2
The second equation is multiplied by 2 to get x + 0.6y = 0.4
Want to reduce - 16 / 15y = - 1.6
y=0.5,x=0.1
How to calculate (2Y square - 4Y + 1) + (- 1 + 4y-2y Square)?
Original formula = 2Y square - 4Y + 1-1 + 4y-2y square
=0
2. Find the positive integer solution of the equation: ① 5x + 7Y = 87, ② 5x + 3Y = 110
3. A piece of steel with a length of 10000 mm should be cut into two kinds of blanks of different specifications. The blank of type A is 300 mm long and the blank of type B is 250 mm long. How many kinds of cutting methods can make full use of the steel?
4. Three brothers, the eldest is 20 years old. The sum of two times the age of the second and five times the age of the third is 97
5. Which of the following equations has no integer solution
① 4x＋2y=11,②10x-5y=70,③9x+3y=111,
④18x-9y=98,⑤91x-13y=169,⑥120x+121y=324.
6. There are 20 multiple-choice questions in an examination record. If you choose right, you will get 5 points. If you choose wrong, you will get 2 points. If you don't answer, you will get 0 point. If you don't answer, you will get 48 points. What's the most he can get?
4.20 16 15 2A + 5B = 97, 97's single digit is 7, 2a and 5b's single digit addition also if 7, a number * 5, the single digit can only be 0 or 5.0, because 2A's single digit can't be 7.5B's single digit is 5, that is to say, B is odd, try slowly, 1-3-5 ----- 11-13-15.. subtract these with 97