SOLUTION: Solve x + y - z = 0 2x - y + z = 6 -x + y + z = 8 Show your answers as (x,y,z)

Algebra ->  Inequalities -> SOLUTION: Solve x + y - z = 0 2x - y + z = 6 -x + y + z = 8 Show your answers as (x,y,z)      Log On


   

Question 84180: Solve
x + y - z = 0
2x - y + z = 6
-x + y + z = 8
Show your answers as (x,y,z)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system and label the equations
x+%2B+y+-+z+=+0 Equation 1
2x+-+y+%2B+z+=+6 Equation 2
-x+%2B+y+%2B+z+=+8 Equation 3
3x=6 Add equations 1 and 2
x=2 Divide both sides by 3

Now lets use this info to find another variable

2%2A2-y%2Bz=6 Plug in x=2 into equation 2 to get Equation 4
4-y%2Bz=6 Multiply
-2%2By%2Bz=8 Plug in x=2 into equation 3 to get Equation 5
-%28-2%2By%2Bz%29=-8 Multiply equation 3 by -1

So now we have the equations
4-y%2Bz=6 Equation 4
2-y-z=-8 Equation 5
6-2y=-2 Add equations 4 and 5
-2y=-8 Subtract 6 from both sides
y=4 Divide both sides by -2

Now lets use this to find z

2%2B4-z=0 Plug in x=2 and y=4 into Equation 1 (at this point any equation will do)
6-z=0 Add
-z=-6 Subtract
z=6 Divide

So our solution is
(2,4,6)