The given system of equations can be solved using substitution. By rearranging the first equation, we can express x in terms of y as x = 34 + 2y. Substituting this value of x into the second equation, we get 34 + 2y - 8y = 12. Simplifying this equation, we find -6y = -22, which implies y = 22/6 = 11/3. Substituting this value of y back into the first equation, we find x = 34 + 2(11/3) = 34 + 22/3 = 136/3. Therefore, the solution to the system of equations is (136/3, 11/3), which is not one of the given answer choices. Thus, the correct answer is infinitely many solutions.