Answer
$(\sqrt[4] {\frac{2}{5}}, \sqrt[4] {\frac{2}{3}}),(-\sqrt[4] {\frac{2}{5}}, \sqrt[4] {\frac{2}{3}}),(\sqrt[4] {\frac{2}{5}}, -\sqrt[4] {\frac{2}{3}}),(-\sqrt[4] {\frac{2}{5}},-\sqrt[4] {\frac{2}{3}})$
Work Step by Step
1. Add up the two equations to get $2/x^4=5$ or $x^4=\frac{2}{5}$, thus $x=\pm\sqrt[4] {\frac{2}{5}}$
2. Take the difference between the two equations to get $2/y^4=3$ or $y^4=\frac{2}{3}$, thus y$=\pm\sqrt[4] {\frac{2}{3}}$
3. Combine the above results to get the real solutions $(\sqrt[4] {\frac{2}{5}}, \sqrt[4] {\frac{2}{3}}),(-\sqrt[4] {\frac{2}{5}}, \sqrt[4] {\frac{2}{3}}),(\sqrt[4] {\frac{2}{5}}, -\sqrt[4] {\frac{2}{3}}),(-\sqrt[4] {\frac{2}{5}},-\sqrt[4] {\frac{2}{3}})$
