Question

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

Answer 1

x+y+z=6 x-y+z=8 x+y-z=0
x+y+x+z=6 y=x+z-8 x+y=z
2x+2y=6 y=3-y+z-8 3-y+y=z
x+y=3 2y=3+3-8 3=z
x=3-y 2y=-2 z=3
x= 4 y=-1

Answer 2

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