$\begin{array}{l}y=-5 x+7 \\ 2 x-2 y=-2\end{array}$

Step 1 ：The given system of equations is \(y = -5x + 7\) and \(2x - 2y = -2\).

Step 2 ：We can use the substitution method to solve this system since the first equation is already solved for y.

Step 3 ：Substitute \(y = -5x + 7\) into the second equation and solve for x.

Step 4 ：The solution for x is \(x = y - 1\).

Step 5 ：Substitute the value of x into the first equation to find the value of y.

Step 6 ：The solution for y is \(y = 2\).

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = 1}\) and \(\boxed{y = 2}\).