\( \begin{array}{l}3 x-4 y=6 \\ 6 x-8 y=10\end{array} \) The system shown has ___ solution(s) infinite one

The two equations in the system are \(3x - 4y = 6\) and \(6x - 8y = 10\). If we multiply the first equation by 2, we get \(6x - 8y = 12\). Now, if we compare this with the second equation \(6x - 8y = 10\), we can see that they have the same left-hand side but different right-hand sides. This indicates that the two lines are parallel and will never intersect, resulting in no solutions. Moreover, when two lines are parallel in a system of linear equations, they simply don't touch each other at any point on the graph, reinforcing the fact that there are no points that satisfy both equations at the same time. So, the system has zero solutions!