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)