$\left\{\begin{array}{l}x y=2 \\ x^{2}+y^{2}=4\end{array}\right.$
\(\boxed{(-\sqrt{2}, -\sqrt{2})}\) and \(\boxed{(\sqrt{2}, \sqrt{2})}\) are the two solutions for the system of equations
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