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 a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in a graph of an inequality?

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. It contains all points that satisfy all inequalities in the system.

Front

How can you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

Front

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

Back

The boundary line separates the solution set from the non-solution set. Points on one side of the line satisfy the inequality, while points on the other side do not.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is '≥' or '≤', but not included if the inequality is '>' or '<'.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line and does not include points on the line, while 'y ≤ mx + b' uses a solid line and includes points on the line.

Front

How do you find the intersection of two inequalities?

Back

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