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Use exact arithmetic?

Use exact arithmetic to solve the following system:
 
10-3x-y=1,
x+y=0.
 
The book says the answer is (1/1.001, -1/1.001). Please show all your work step by step. Thanks.

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(0.001)x-y = 1                      [10-3 = 0.001]
x+y=0; Therefore y = -x
 
Plugging y = -x into the first equation:
 
(0.001)x -(-x) = 1
 
1.001x = 1
 
x = 1/1.001
 
y = -x = -1/1.001