X + y + Z = 26, X-Y = 1, 2x-y + Z = 18, these three are ternary linear equations. How to solve them, we need to use addition and subtraction elimination method or other methods!

You can solve the equation x + y + Z = 26 (1) X-Y = 1 (2) 2x-y + Z = 18 (3) (1) - (3) - x + 2Y = 8 (4) (4) + (2) y = 9 by substituting y = 9 into (2) and substituting x = 10 into (1) 9 + 10 + Z = 26, z = 7

X + y + Z = 26, X-Y = 1, 2x-y + Z = 18, the answer of ternary linear equation
X + y + Z = 26, X-Y = 1 2x-y + Z = 18, what is the answer to the ternary linear equation?
X + y + Z = 26, X-Y = 1 2x-y + Z = 18, what is the answer to the ternary linear equation?
Accurate solution, accurate solution!

x+y+z=26 ⑴
x-y=1 ⑵
2x-y+z=18 ⑶
⑴+⑵:2x+z=27(4)
⑴+⑶:3x+2z=44(5)
(4)*2-(5):x=10
Substituting (4): z = 7
Substitute (1) y = 9!
I'm so tired!

Ternary linear equations: x + y + Z = 18. X-Y = - 1,2x + Z-Y + 26

x+y+z=18 ①
x-y=-1 ②
2x+z-y=26 ③
① + 2: 2x + Z = 17 4
② - 3 is: - x-z = - 27 5
④ + 5: x = - 10
Substituting x = - 10 into ② to get: - 10-y = - 1, then: y = - 9
Substituting x = - 10 into 4 to get: - 20 + Z = 17, then: z = 37
Therefore, the solutions of the original equations are: x = - 10, y = - 9, z = 37

To solve the system of linear equations x + y + Z = 26 X-Y + XZ = 1 2x-y + Z = 18
It's x + y + Z = 26, X-Y + 2Z = 1 2x-y + Z = 18.
x-y/2-9=y/3 3（x+y）=2（x+y）-2

x+y+z=26①
x-y+2z=1 ②
2x-y+z=18 ③
① + 2, get 2x + 3Z = 27, 4
① In addition, we get 3x + 2Z = 44
④ The solution is 4x-9x = 54-132 and x = 15.6
Substituting into 4, the solution is Z = - 1.4
Substituting ①, the solution is y = 11.8

To solve the ternary linear equations 1. X + y + Z = 142 30 / x + 28 / y + 35 / z = 4.5 30 / x + 35 / y + 28 / z = 4.7
Urgent... Brothers and sisters! Quick

Let x = 1 / A
y+z=142-1/a(1)
28/y+35/z=4.5-30a(2)
35/y+28/z=4.7-30a(3)
(2):
28z+35y=(4.5-30a)yz
35z+28y=(4.7-30a)yz
The results are as follows
z=63/(3.7-a) y=63/(5.5-a)
Substituting (1)
1/a+63/(5.5-a)+63/(3.7-a)=142
Solving cubic equation of one variable

To solve the linear equations of three variables: x + y = 28; x-z = 12; Z + y = 16. X = 23, y = 5, z = 11

Any two equations can deduce another one, so in fact, there are only two equations for this system of equations, while the system of two equations with three unknowns can have innumerable solutions
If you don't believe me, try these solutions (x, y, Z in turn)
1,27,-11
2,26,-10
3,25,-9
4,24,-8
5,23,-7
.

X * (Y-Z) = 27, y * (x-z) = 35, Z * (x + y) = 28 positive integer solutions of three equations

The results are as follows
xy=45
Substituting them separately, we get
xz=18
yz=10
Comparison of the latter two formulas
x/y=9/5
Positive integer solution,
x=9,y=5,z=2

Ternary linear equations X: y = 3:4, Y: z = 4:5, x + y + Z = 36

x:y=3:4
x=3y/4 (1)
y:z=4:5
z=5y/4 (2)
(1) (2) substitute: x + y + Z = 36
3y/4+y+5y/4=36
3y=36
y=12
x=9
z=15
The solutions of the equations are: x = 9, y = 12, z = 15

How to solve the system of linear equations (1) x + Y-Z = 11, y + z-x-5, Z + X-Y = 1

Is the equal sign after the second equation written as a minus sign?
The solution of ternary linear equations is the same as that of binary linear equations
Elimination
Here, by adding the first two equations, X and Z can be eliminated, and the solution is y = 8
Substituting y = 8 into the original equations is a system of linear equations of two variables?
The solution is x = 6, y = 8, z = 3

What is the solution of the system of linear equations with three variables {y = 2x + y = 0, X-Y-Z = 0?

y=2
x+y=0,x=-y=-2
x-y-z=0
z=x-y=-2-2=-4
So x = - 2, y = 2, z = - 4

X + y + Z = 26, X-Y = 1, 2x-y + Z = 18, these three are ternary linear equations. How to solve them, we need to use addition and subtraction elimination method or other methods!