\begin{tabular}{l} A system of equations is graphed on the coordinate plane. \\ \( \begin{array}{l}2 y=3 x-1 \\ 4 y=6 x-2 \\ \text { Select the number of solutions for the system of equations from } \\ \text { the drop-down menu. } \\ \text { Choose. } \\ \text { Choose. } \\ \text { no solution } \\ \text { one solution } \\ \text { intintely many solutions }\end{array} \) \\ \hline\end{tabular}

When analyzing the two equations given, you'll notice they can be simplified. The first equation, \(2y = 3x - 1\), can be rewritten as \(y = \frac{3}{2}x - \frac{1}{2}\). The second equation, \(4y = 6x - 2\), simplifies to \(y = \frac{3}{2}x - \frac{1}{2}\) as well. Since both equations represent the same line, every point on this line is a solution, leading to infinitely many solutions! This scenario is akin to two hikers marking the same path on a map; there's not just one way to reach the peak—embrace the journey of possibilities! Keep in mind that when both equations yield the same slope and y-intercept, they'll always overlap in every direction. It's like walking on parallel lines that eventually meet at every point along their shared path!