Use exact arithmetic?

Question

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.

Answer 1

(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