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A system of inequalities consists of multiple inequalities that are considered together. Each inequality within the system contributes its own conditions to the set of possible solutions. For example, solving a system with two inequalities requires that a solution must satisfy both conditions simultaneously.

When graphing a system of inequalities, you'll graph each inequality separately and identify the overlapping region that satisfies all of them. This shared region indicates where all of the inequalities are true at once and is the solution to the system. To succeed with systems of inequalities, visualize each individual inequality first and then look for the composite area that adheres to all the given restrictions.

Understanding inequality notation is key to solving and graphing inequalities accurately. Inequalities are mathematical expressions that show the relationship between two values, with one being greater than, less than, greater than or equal to, or less than or equal to another.

The symbols used are: '<' for 'less than', '>' for 'greater than', '' for 'less than or equal to', and '≥' for 'greater than or equal to'. For example, in the given exercise, ' is used to express that the y-values are strictly greater than the values of the function `2x + 3`. It is essential to identify the type of inequality to determine the correct graphing approach, such as whether to use dashed or solid lines when drawing the boundary line.

The boundary line in the context of graphing inequalities is the line that represents the edge where the inequality transitions from true to false or vice versa. For inequalities with a '<' or '>' sign, you use a dashed line to represent that points on the line are not included in the solution set. Conversely, for inequalities including '=,' a solid line is used, indicating that points on the line satisfy the inequality.

In our exercise example, the equation ' yields a boundary line that should be dashed because 'y > 2x + 3' does not include solutions where 'y' equals '2x + 3'. Properly drawing and identifying the boundary line is a critical step in visualizing the solution set.

A solution region is the area on a graph in which all points satisfy the inequality or system of inequalities. After drawing the boundary line(s), you can identify the solution region by selecting a test point (not on the boundary) and substituting its values into the inequality.

If the inequality holds true with the test point, then the area that includes that point is the solution region. Otherwise, the opposite side is the solution region. In the exercise with the inequality 'y > 2x + 3', the solution region is the area above the boundary line since it contains all points where 'y' value is greater than '2x + 3'. Remember to shade this region to clearly indicate to anyone viewing your graph where the solutions can be found.