(1) \( \left\{\begin{array}{l}y \geq 4 x \\ 2 y \leqslant 5-3\end{array}\right. \)

To start off, let's simplify the second inequality in the system. The expression \( 5 - 3 \) simplifies to \( 2 \), so we have \( 2y \leq 2 \), which means \( y \leq 1 \). Now, you have two inequalities: \( y \geq 4x \) and \( y \leq 1 \). To find the feasible region, you would plot both lines on a coordinate graph and identify where they intersect and overlap. Now for a common mistake: students often forget to check whether the inequalities restrict the same region effectively. For instance, here, \( y \geq 4x \) suggests that the area above the line is valid, while \( y \leq 1 \) limits it to below the horizontal line. Since there are no points that satisfy both conditions simultaneously (as the line \( 4x \) will always yield a y-value larger than 1 for any x), it’s crucial to remember to interpret the intersections and boundaries correctly—sometimes they can show that there's no feasible solution at all!