What is the solution of the following system? {x+y+z=6, x-y+z=8, x+y-z=0

Much easier to use elimination method to solve this problem

Given system of equation
x + y + z = 6   (this is first equation)
x - y + z = 8    (this is second equation)
x + y - z = 0    (this is third equation)

FIRST
I'm going to eliminate x and y from the first and third equation to find the value of z
x + y + z = 6
x + y - z  = 0
- (substract)
          2z = 6
            z = 3
The value of z is 3

SECOND
I'm going to x and z from the first and third equations to find the value of y.
x + y + z = 6
x - y  + z = 8
- (substract)
    2y        = -2
      y        = -1
The value of y is -1

THIRD
I'm going to use subtitution method to find x. I'm subtituting the value of y and z to one of the equation.
x + y + z = 6
x + (-1) + 3 = 6
x + 2 = 6
x = 4
The value of x is 4

The solution is (4,-1,3)
x = 4
y = -1
z = 3