Solving linear equations of three variables x-2y+z=0 .(1) 3x+y-2z=0.(2) 7x+6y+7z=100...(3)

Solving linear equations of three variables x-2y+z=0 .(1) 3x+y-2z=0.(2) 7x+6y+7z=100...(3)

X-2y + Z = 0. (1) 3x + y-2z = 0. (2) 7x + 6y + 7z = 100... (3) x = 2y-z from (1). (4) substituting (4) into (2) and (3) to get 3 (2y-z) + y-2z = 07 (2y-z) + 6y + 7z = 100, finishing 7y-5z = 0. (5) 20Y = 100. (6) substituting (6) into (5) to get y = 100 △ 20 = 5, y = 5 to get 7 × 5-5z = 05z = 7, y = 5, z = 7

To solve a system of linear equations of three variables,
x:y:z=3:4:5
x+y+z=36

x: If y = 3:4, x = 3 / 4Y
y: If z = 4:5, then z = 5 / 4Y
Substitute x + y + Z = 36 to get
3/4y+y+5/4y=36
So 3Y = 36, y = 12
x=9,z=15

Exercises of ternary linear equations

2x+y-z=2
x+2y-z=5
x-y+2z=-7
2x+y-z=2---① x+2y-z=5---② x-y+2z=-7---③
①-②:x-y=-3---④
②-③:x+y=1---⑤
The solution of (4) and (5) is: x = - 1, y = 2
Then, any equation in the original system of equations is brought in, and the solution is Z = - 2

A few questions about the system of linear equations of three variables

3x+2y-a=20
2x-2a=4
5x-6y=1

Solving problems of linear equations of three variables
In the equation y = AX2 + BX + C, when x = 1, y = - 2; when x = - 1, y = 20; when x = 3 / 2 and x = 1 / 3, the values of Y are equal, and the values of a, B and C are obtained

-If y is the same, then x = (3 / 2 + 1 / 3) / 2 = 11 / 12, y = 0, so 121a / 144 + 11b / 12 + C = 0121a + 132b + 12C = 0 (3) (1) - (2) 2B = - 22b = - 11 (1) + (2) a + C = 9C = 9-A, so 121a-1452 + 108-12a = 0109A = 1344a = 1344 / 109C = - 363 / 109

Problems of linear equations with three variables
1） x+y=z
x+2y+2z=3
2x-3y+2z=5
2)2x+3y+z=1
x+y+z=-2
3x-2y-z=-4

1、x=22/19,y=-7/19,z=15/19
The first equation can be substituted into the second and third equations respectively. First, Z is eliminated, and then the addition and subtraction elimination method is used to solve the binary linear equations
The second problem also can use this method. Oneself practice

Given (a + b) / 3 = (2C-B) / 4 = (2a + C) / 5, find the value of (a + b) / C

Let (a + b) / 3 = (2C-B) / 4 = (2a + C) / 5 = K
be
(a+b)=3k (1)
2c-b=4k (2)
2a+c=5k (3)
(1) + (2) get
2c+a=7k （4）
2 (4) - (3)
3c=9k
c=3k
therefore
（a+b）/c=3k/(3k)=1

Given 2A = 3, 2b = 5, 2C = 30, find the relationship between a, B, C

∵2a=3，2b=5，2c=30，∴2a⋅2b=15，∴2⋅2a⋅2b=30，∴2a+b+1=2c，∴a+b+1=c．

Given a: B: C: = 4:5:6, and a + b-2c = 3, then the value of B

Let a = 4x
a:b:c:=4:5:6=4x:5x:6x
a+b-2c=3
4x+5x-2*6x=3
-3x=3
x=-1
Then B = - 5

If the absolute value of a number is equal to the opposite of the number, then the number is ()
A. Positive number B. negative number C. positive number, zero D. negative number, zero

Let the rational number be a, then according to the meaning of the question: | a | = - A, so a ≤ 0, that is to say, the rational number is not positive