Use 3-digit arithmetic with no pivoting?

[Math10]

Homework Statement

Use 3-digit arithmetic with no pivoting to solve the following system:

10^-3x-y=1,
x+y=0.

Homework Equations

I know that 10^-3=0.001.

The Attempt at a Solution

The answer for this problem is (0, -1).
Here's the work:
1.001 0
1 1

I've set the augmented matrix and tried using the Gauss-Jordan method to solve the system but I got x=1/1.001 and y=-1/1.001, of course that's not the answer. How do I do this problem?

 

[Mogarrr]

Using Gauss-Jordian method, the matrix you should start off with is

\begin{pmatrix} 10^{-3} & -1 & 1 \\ 1 & 1 & 0 \end{pmatrix}

 

[Math10]

Thank you. Don't answer this question anymore. I've already solved it. Thanks again, everyone.

 

[HallsofIvy]

I wouldn't bother with matrices. Subtracting .001x+ y= 0 from x+ y= 1, y is eliminated, and we have .999x= 1. Divide both sides by .999, stopping at three decimal places.