Systems of Inequalities

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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line represents that the points on the line are included in the solution set, indicating that the inequality is 'greater than or equal to' or 'less than or equal to'.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' or 'less than'.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

How can you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a solid or dashed line based on the inequality. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

Front

What is the significance of the point (1, 0) in the context of a system of inequalities?

Back

The point (1, 0) is a solution to the system of inequalities, meaning it satisfies all the inequalities in the system.

Front

What does it mean if a point is not a solution to a system of inequalities?

Back

If a point is not a solution, it means that when you substitute its coordinates into the inequalities, at least one inequality is not satisfied.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is not included, while 'greater than or equal to' (≥) means the value is included in the solution set.

Front

What is the difference between 'less than' and 'less than or equal to'?

Back

'Less than' (<) means the value is not included, while 'less than or equal to' (≤) means the value is included in the solution set.