$\left\{\begin{array}{l}x y=2 \\ x^{2}+y^{2}=4\end{array}\right.$

Step 1 ：First, solve the first equation for x: \(x = \frac{2}{y}\)

Step 2 ：Substitute this expression for x into the second equation: \(\left(\frac{2}{y}\right)^2 + y^2 = 4\)

Step 3 ：Solve this equation for y: \(y = \pm\sqrt{2}\)

Step 4 ：Find the corresponding x values: \(x = \pm\sqrt{2}\)

Step 5 ：\(\boxed{(-\sqrt{2}, -\sqrt{2})}\) and \(\boxed{(\sqrt{2}, \sqrt{2})}\) are the two solutions for the system of equations