Step 1 :The system of equations is given by: \(x = 3y + 3\) and \(x = 8y - 7\).
Step 2 :We can solve this system by substitution. Since both equations are already solved for \(x\), we can set them equal to each other and solve for \(y\).
Step 3 :Setting the two equations equal to each other gives us \(3y + 3 = 8y - 7\).
Step 4 :Solving this equation for \(y\) gives us \(y = 2\).
Step 5 :Substituting \(y = 2\) into either of the original equations to find the value of \(x\) gives us \(x = 9\).
Step 6 :Final Answer: The solution set is \(\boxed{(9, 2)}\).