In the system shown below, what are the coordinates of the solution that lies in quadrant i? x^2-y^2=25, x+y=25

The given equations in this item are,
                     x² - y² =25
and 
                    x + y = 25

It can be deduced that the first equation is a difference of two squares and can be factored out as that one shown below.
           (x - y)(x + y) = 25

From the second equation, x+y = 25. Substituting this to the equation above,
             (x-y)(25) = 25
Hence, x - y = 1

The system of linear equations is,
                  x + y = 25
                  x - y = 1
Adding the equations together,
         2x = 26
        x = 13

The value of y is 12.

Since both x and y are positive values then, this solution lies in the first quadrant.

ANSWER: (13,12)

25. 22 + 1 2 25