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## Homework Statement

system of equations is as follows

x+y=1

2x+y-z=1

3x+y-2z=1

##\begin{cases} x+y=1 |*(-1)\\2x+y-z=1\\3x+y-2z=1 \end{cases}##

## Homework Equations

Gaussian elimination method technique

## The Attempt at a Solution

##\begin{cases} x+y=1 \\ x-z=0 |*(-2)\\ 2x-2z=0 \end{cases}##

<=>

##\begin{cases} x+y=1 |*(-1)\\ x-z=0 \\ 0=0 \end{cases}##

<=>

##\begin{cases} x+y=1 \\ -y-z=-1 \\ x=z \end{cases}##

<=>

at this stage I think you are supposed to plug in x=z into some equation in the system

##\begin{cases} x+y=1 \\ -y-z=-1 \\ x=z \end{cases}##

##\begin{cases} x+y=1 <=> x=1-y \\ -y-z=-1 \\ x=z \end{cases}##

##-y-x=-1##

<=> x=-y+1

from those two equations it can be seen that those equations at least are identical equations for the same line.

So I think ultimately based on that geometry there should be infinite solutions (is that the correct way to do it and solve it?)