Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that involve 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 it mean if an inequality is represented with a dashed line on a graph?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does it mean if an inequality is represented with a solid line on a graph?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line will be shaded to represent the solution set.

Front

What is the solution set of the system: y > 2x - 4 and y < 2?

Back

The solution set includes all points that are above the line y = 2x - 4 and below the line y = 2.

Front

How can you identify a solution that is NOT part of a system of inequalities?

Back

A point that does not satisfy at least one of the inequalities in the system is not part of the solution set.

Front

What is the significance of the boundary line in a system of linear inequalities?

Back

The boundary line separates the solution set from the non-solution set, indicating where the inequalities change from true to false.

Front

What does the inequality y < 2x - 4 represent graphically?

Back

It represents the area below the line y = 2x - 4, with a dashed line indicating that points on the line are not included.

Front

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

Back

'Greater than' (>) means the boundary is not included (dashed line), while 'greater than or equal to' (≥) means the boundary is included (solid line).