Пожалуйста, нужна помощь с системой

Question 1

Question 2

Решите задачу:

$\left \{ {{|x|-|y|=4} \atop {x^2+y^2=41}} \right. \\\\Formyla:\quad |x|^2=x^2\; ,\; \; |y|^2=y^2\; .\\\\ \left \{ {{|x|-|y|=4} \atop {|x|^2+|y|^2=41}} \right. \qquad Zamena:\; \; t=|x|\; ,\; \; p=|y|\; \; \to \left \{ {{t-p=4} \atop {t^2+p^2=41}} \right. \\\\(t-p)^2=16\; \; \to \; \; \; t^2-2tp+p^2=16\; ,\; \; (\underbrace {t^2+p^2}_{41})-2tp=16\\\\2tp=41-16\; ,\; \; 2tp=25$

$\left \{ {{t-p=4} \atop {2tp=25}} \right. \; \left \{ {{t=p+4} \atop {2p(p+4)=25}} \right. \; \left \{ {{t=p+4} \atop {2p^2+8p-25=0}} \right.$

$2p^2+8p-25=0\; ,\; \; \; D/4=4^2-2(-25)=66\\\\p_1=\frac{-4-\sqrt{66}}{2}=-2-\frac{\sqrt{66}}{2}\; ,\; \; p_2=\frac{-4+\sqrt{66}}{2}=-2+\frac{\sqrt{66}}{2}\\\\t_1=p_1+4=2-\frac{\sqrt{66}}{2}\; ,\; \; t_2=p_2+4=2+\frac{\sqrt{66}}{2}\\\\Tak\; kak\; |x| \geq 0\; \; i\; \; |y| \geq 0\; ,\; a\; \; t_1\ \textless \ 0\; ,\; p_1\ \textless \ 0,\\\\to \; \; t_1\; \; i\; \; p_1\; \; ne\; \; podxodyat.\\\\|x|=2+\frac{\sqrt{66}}{2}\; ,\; \; \; ,\; |y|=-2+\frac{\sqrt{66}}{2}$

$x=\pm \Big (2+\frac{\sqrt{66}}{2}\Big )\; ,\; \; \; y=\pm \Big (-2+\frac{\sqrt{66}}{2}\Big )$

$Otvet:\; \; \Big (2+\frac{\sqrt{66}}{2}\; ;\; -2+\frac{\sqrt{66}}{2}\Big )\; ,\; \Big (2+\frac{\sqrt{66}}{2}\; ;\; 2-\frac{\sqrt{66}}{2}\Big )\; ,\\\\\Big (-2-\frac{\sqrt{66}}{2}\; ;\; -2+\frac{\sqrt{66}}{2}\Big )\; ,\; \; \Big (-2-\frac{\sqrt{66}}{2}\; ;\; 2-\frac{\sqrt{66}}{2}\Big )\; .$