Question 1131189
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 x^2 - y^2 = 15     (1)
4x^2 + y^2 = 65.    (2)

------------------------ Add the equations.  In this way you eliminate y^2 


5x^2 = 15 + 65,


5x^2 = 80,


x^2 = 80/5 = 16  ====>  x = +/- {{{sqrt(16)}}} = +/- 4.


Then from eq(1),  y^2 = x^2 - 15 = 16 - 15 = 1  ====>  y = +/- {{{sqrt(1)}}} = +/- 1.


<U>Answer</U>.  The numbers are  (4,1),  (-4,1),  (4,-1)  and  (-4,-1).  In all, there are 4 solutions.
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