How to solve two 2 variable quadratics using system of equations?

Question

Given $\left\{\begin{array}{rcrcr} {\displaystyle\left(x + 2\right)^{2}} & {\displaystyle +} & {\displaystyle\left(y - 2\right)^{2}} & {\displaystyle = } & {\displaystyle 9} \\[1mm] {\displaystyle\left(x - 2\right)^{2}} & {\displaystyle +} & {\displaystyle\left(y + 2\right)^{2}} & {\displaystyle = } & {\displaystyle 25} \end{array}\right. $

Find the two solutions for $\left(x,y\right)$. How do I do this ?.

Answer 1

Write $$x^2+y^2+4x-4y=1$$ $$x^2+y^2-4x+4y=17$$ and compute eqn2-eqn1: so $$-8x+8y=16$$ Can you proceed?

Answer 2

Difference of two terms gives: $8x-8y=-16\iff x=y-2$. By substitution $(x+2)^2+x^2=9$. Now expand and solve for x.