Question

solve x+y+z=8 x-y-z=4 -x+y-z=8

Answer 1

x+y+z=8
x-y-z=4
-x+y-z=8
Process of elimination.
x+y+z=8
x-y-z=4
Add
2x=12
Divide
x=6
~~~~~~~~~~~~~~~
(x-y-z=4) times -1
-x+y+z=-4
-x+y-z=8
Add
-2x+2y=4
~~~~~~~~~~~~~~~~
(x=6) times 2
2x=12
-2x+2y=4
Add
2y=16
Divide
y=8
~~~~~~~~~~~~~~
Substitute answers into original equation.
6+8+z=8
14+z=8
Subtract
z=-6
~~~~~~~~~~~~~~~~~~~
Substitute all variable answers in to all equations to see if correct.
6+8+(-6)=8
14-6=8
8=8 Correct!
6-8-(-6)=4
-2-(-6)=4
-2+6=4
4=4 Correct!
-6+8-(-6)=8
2-(-6)=8
2+6=8
8=8 Correct!
~~~~~~~~~~~~~~~~~~
So
x=6
y=8
z=-6

Answer 2

Get it?