SOLUTION: Use row operations to solve the system. x+y-z=2 3x-y+z=2 x-4y+2z=-35 A. This system has exactly one solution. The solution is (__,__,__) B. This system has infinitely ma

Algebra ->  College  -> Linear Algebra -> SOLUTION: Use row operations to solve the system. x+y-z=2 3x-y+z=2 x-4y+2z=-35 A. This system has exactly one solution. The solution is (__,__,__) B. This system has infinitely ma      Log On


   

Question 1087356: Use row operations to solve the system.
x+y-z=2
3x-y+z=2
x-4y+2z=-35

A. This system has exactly one solution. The solution is (__,__,__)
B. This system has infinitely many solutions of the form (__,__,z) where z is any real number.
C.This system has no solution.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Add R1 and R2,
x%2By-z%2B3x-y%2Bz=2%2B2
4x=4
x=1
So then the equations become,
4.y-z=1
5.-y%2Bz=-1
-4y%2B2z=-36
6.-2y%2Bz=-18
Adding 4 and 6,
y-z-2y%2Bz=1-18
-y=-17
y=17
Now solve for z using any of the equations.
The system has exactly one solution.