SOLUTION: Solve for x, y and z x + y + z = 2 x + 2y - z = 5 3x - y = 16 answer: (x;y;z) = ( ; ; )

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve for x, y and z x + y + z = 2 x + 2y - z = 5 3x - y = 16 answer: (x;y;z) = ( ; ; )      Log On


   

Question 369509: Solve for x, y and z
x + y + z = 2
x + 2y - z = 5
3x - y = 16
answer: (x;y;z) = ( ; ; )
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x+%2B+y+%2B+z+=+2
2.x+%2B+2y+-+z+=+5
3.3x+-+y+=+16
Add eq. 1 and 3 together,
x%2By%2Bz%2Bx%2B2y-z=2%2B5
4.2x%2B3y=7
Multiply eq. 3 by 3 and add to eq. 4,
9x-3y%2B2x%2B3y=48%2B7
11x=55
highlight%28x=5%29
Then from eq. 3,
15-y=16
highlight%28y=-1%29
Then from eq. 1,
5-1%2Bz=2
highlight%28z=-2%29