Solve the system by the addition method.
\[
\begin{array}{l}
8 x+2 y=8 \\
2 x+5 y=-16
\end{array}
\]
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The solution set is (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is $\{(x, y) \mid \square\}$. (Type an equation.)
C. There is no solution. The solution set is $\varnothing$.

Step 1 ：The given system of equations is a linear system. The addition method, also known as the elimination method, is a way to solve a system of linear equations. This method adds or subtracts the equations in order to eliminate one of the variables, making it possible to solve for the other variable.

Step 2 ：The first step is to multiply the equations by necessary multiples such that the coefficients of y's or x's in both equations will cancel each other out when added. In this case, we can multiply the first equation by 5 and the second equation by 2. This will give us coefficients of 10 for y in both equations.

Step 3 ：Then, we subtract the second equation from the first to eliminate y. This will give us the equation \(36x = 72\).

Step 4 ：Solving for x, we get \(x = 2\).

Step 5 ：Finally, we substitute x into one of the original equations to solve for y. This gives us \(y = -4\).

Step 6 ：Final Answer: \(\boxed{(2, -4)}\)