Determine the number of solutions the system has. \( \begin{array}{l}4 x-8 y=16 \\ 6 x-12 y=5\end{array} \) Select Choice

To determine the number of solutions for the system of equations, we can analyze the relationship between the two equations. The first equation can be simplified by dividing everything by 4, resulting in: \( x - 2y = 4 \). The second equation can be simplified by dividing everything by 6, yielding: \( x - 2y = \frac{5}{6} \). Now, if we look at both simplified equations, we see that they represent two lines that have the same slope (1 for both) but different y-intercepts (4 and 5/6). Thus, these lines are parallel and will never intersect, indicating that there are no solutions to the system. So the system of equations has no solutions (inconsistent system).