SOLUTION: The difference between the squares of two numbers is 15. Four times the square of the first number increased by the square of the second number is 65. Find the numbers.

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Question 1131189: The difference between the squares of two numbers is 15. Four times the square of the first number increased by the square of the second number is 65. Find the numbers.
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
 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%2816%29 = +/- 4.


Then from eq(1),  y^2 = x^2 - 15 = 16 - 15 = 1  ====>  y = +/- sqrt%281%29 = +/- 1.


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