$\left\{\begin{array}{l}5 x-2 y=2 \\ x+2 y=2\end{array}\right.$

Step 1 ：Given the system of equations: \(\begin{cases} 5x - 2y = 2 \ x + 2y = 2 \end{cases}\)

Step 2 ：We can solve this system by using the elimination method. By adding the two equations, we can eliminate y and solve for x.

Step 3 ：Adding the two equations gives us: \(6x = 4\)

Step 4 ：Solving for x, we get: \(x = \frac{2}{3}\)

Step 5 ：Substituting \(x = \frac{2}{3}\) into the second equation, we get: \(\frac{2}{3} + 2y = 2\)

Step 6 ：Solving for y, we get: \(y = \frac{2}{3}\)

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = \frac{2}{3}, y = \frac{2}{3}}\)