Graphing Systems of Inequalities 2024-25

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions to that inequality, typically shaded to indicate the region that satisfies the inequality.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What does it mean when a solution set is represented on one side of a line in a graph?

Back

It means that all points on that side of the line satisfy the inequality represented by the line.

Front

How do you graph the inequality y > 2x - 4?

Back

1. Graph the line y = 2x - 4 as a dashed line (since it's 'greater than'). 2. Shade the area above the line to represent all points where y is greater than 2x - 4.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set (for '>' or '<'). A solid line indicates that points on the line are included (for '≥' or '≤').

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution to the system.

Front

What does the term 'solution set' refer to in the context of inequalities?

Back

The solution set refers to all the points that satisfy the given inequalities in a system.

Front

How can you tell which points are part of the solution set?

Back

By substituting the coordinates of the points into the inequalities. If they satisfy all inequalities, they are part of the solution set.