Solve the System by Elimination/Addition
\[
\left\{\begin{array}{l}
2 x-2 y=20 \\
-3 x+8 y=-55
\end{array}\right.
\]
No solution
Infinite number of solutions

Step 1 ：The system of equations is given as follows: \[\left\{\begin{array}{l} 2 x-2 y=20 \\ -3 x+8 y=-55 \end{array}\right.\]

Step 2 ：We solve this system by the method of elimination. This involves adding or subtracting the equations in order to eliminate one of the variables, making it possible to solve for the other variable.

Step 3 ：Let's denote the first equation as eq1 and the second equation as eq2. So, eq1 = \(2x - 2y = 20\) and eq2 = \(-3x + 8y = -55\).

Step 4 ：Solving these equations, we find the solution as \(x = 5\) and \(y = -5\). This means that these values of x and y satisfy both equations simultaneously.

Step 5 ：Final Answer: The solution to the system of equations is \(\boxed{x = 5}\) and \(\boxed{y = -5}\).