\( \begin{array}{l}y=2 x+3 \\ 2 y=4 x+6\end{array} \) The system of equations has \( \quad \) infinite one no

The equations \(y = 2x + 3\) and \(2y = 4x + 6\) are actually the same line. If you manipulate the second equation by dividing everything by 2, you’ll see it simplifies to \(y = 2x + 3\). This means that there are infinitely many solutions since every point on the line is a solution! In the realm of linear equations, when two equations represent the same line, they are considered dependent, leading to infinite solutions. To visualize this, you could graph both equations on the same set of axes—surprise! They overlap completely, confirming they are one and the same!