Answer: The required solution set is
(x, y) = (3, 4), (-3, 4), (3, -4) and (-3, -4).
Step-by-step explanation: We are given to solve the following system :

We will be using the method of Elimination to solve the problem.
Adding equations (i) and (ii), we have
![(x^2+y^2)+(y^2-x^2)=25+7\\\\\Rightarrow 2y^2=32\\\\\Rightarrow y^2=16\\\\\Rightarrow y=\pm\sqrt{16}~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow y=\pm4.](https://tex.z-dn.net/?f=%28x%5E2%2By%5E2%29%2B%28y%5E2-x%5E2%29%3D25%2B7%5C%5C%5C%5C%5CRightarrow%202y%5E2%3D32%5C%5C%5C%5C%5CRightarrow%20y%5E2%3D16%5C%5C%5C%5C%5CRightarrow%20y%3D%5Cpm%5Csqrt%7B16%7D~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Btaking%20square%20root%20on%20both%20sides%7D%5D%5C%5C%5C%5C%5CRightarrow%20y%3D%5Cpm4.)
From equation (ii), we get
![(\pm4)^2-x^2=7\\\\\Rightarrow 16-x^2=7\\\\\Rightarrow x^2=16-7\\\\\Rightarrow x^2=9\\\\\Rightarrow x=\pm\sqrt9~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm3.](https://tex.z-dn.net/?f=%28%5Cpm4%29%5E2-x%5E2%3D7%5C%5C%5C%5C%5CRightarrow%2016-x%5E2%3D7%5C%5C%5C%5C%5CRightarrow%20x%5E2%3D16-7%5C%5C%5C%5C%5CRightarrow%20x%5E2%3D9%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cpm%5Csqrt9~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Btaking%20square%20root%20on%20both%20sides%7D%5D%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cpm3.)
Thus, the required solution set is
(x, y) = (3, 4), (-3, 4), (3, -4) and (-3, -4).