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When working with a system of inequalities, you're essentially looking at multiple inequalities simultaneously and trying to find a set of values that satisfies all of the inequalities in the system. Imagine you're at a buffet with a variety of dishes, each with a limit on how much you can eat. A system of inequalities is like trying to fill your plate without taking too much of any one dish so that you adhere to all limits—just like finding values that fit within all the given numerical 'limits'.

Graphing a system of inequalities is a visual method to identify the so-called 'common ground' where all conditions are met. This involves plotting each inequality on the same set of axes and looking for the overlapping region that represents solutions to the entire system. It's essential to accurately represent each inequality with shading or boundary lines to understand where these regions overlap. In our exercise, there is only one inequality, making it a simple system, but the fundamental principles apply when handling multiple inequalities. We plot them on a graph and look for overlapped areas that satisfy all inequalities in the system.

Inequality notation is the system we use to denote the relationships between values, indicating which values are smaller, larger, or within certain bounds. The symbols <, >, \(\leq\), and \(\geq\) are the cornerstones of this notation, representing 'less than', 'greater than', 'less than or equal to', and 'greater than or equal to' respectively. This notation helps us efficiently communicate the range of values that are possible solutions to an inequality.

Understanding the symbols is like learning the rules of the road—knowing which 'directions' are possible to travel. For instance, if we say \(y > -2\), it means that 'y' can be any number as long as it is greater than -2. If we refine it to \(y \leq 5\), we've set an upper bound, indicating 'y' cannot exceed 5, and may include 5 itself. When graphing, an open circle at a value means that value is not included (as with -2 in our exercise), whereas a closed or filled circle denotes inclusion of that value (as with 5).

A solution set is a collection of all possible answers that satisfy a given inequality or system of inequalities. Think of it as a treasure map, where 'X' marks the spot, except on our map, there could be entire regions marked 'X' instead of single points. It tells us which values we're allowed to choose in order to meet the conditions we've been given.

In graphing, the solution set for an inequality is represented visually. For the inequality in our exercise, the solution set includes all values of 'y' between -2 and 5, not including -2, but including 5. This set is depicted as a shaded area between y = -2 and y = 5, showing us at a glance the range of permissible values. The beauty of graphing these solutions is in the immediate visualization it provides. In exercises with more complex systems, identifying the region of overlap between multiple inequalities can visually capture the solution set, making it easier to understand and work with.