Question 1086862
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.