SOLUTION: x+2y-2z=2 3x-2y+2z=-1 x-2y-z=0 A The unique solution to the system is left The system has infinitely many solutions. The solution described in terms of variable z is

Algebra ->  Finance -> SOLUTION: x+2y-2z=2 3x-2y+2z=-1 x-2y-z=0 A The unique solution to the system is left The system has infinitely many solutions. The solution described in terms of variable z is      Log On


   

Question 1086862: x+2y-2z=2
3x-2y+2z=-1
x-2y-z=0
A
The unique solution to the system is left

The system has infinitely many solutions. The solution described in terms of variable z is
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
x+2y-2z=2
3x-2y+2z=-1
x-2y-z=0
A
The unique solution to the system is left
The system has infinitely many solutions. The solution described in terms of variable z is

Solution:
x+2y-2z=2............(1)
3x-2y+2z=-1..........(2)
x-2y-z=0.............(3)

(1)+(2) =>
4x=1 => x=1/4

(1)+(3)
2x-3z=2 =>
2/4-3z=2 [x=1/4] =>
3z=-1/2

Substitute x and z in (1)
1/4+2y-2(-1/2)=2 =>
2y=2-1/4-1=3/4 =>
y=3/8

Therefore there is a unique solution set, S={1/4, 3/8, -1/2}
This conclusion can also be obtained by seeing that the three equations are not linearly dependent.