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 inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does it mean when a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set. This occurs when the inequality is strict (using < or >).

Front

What does it mean when a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set. This occurs when the inequality is non-strict (using ≤ or ≥).

Front

How do you determine the shading direction in a graph of an inequality?

Back

The shading direction is determined by the inequality sign. If the inequality is 'greater than' (>) or 'greater than or equal to' (≥), shade above the line. If it is 'less than' (<) or 'less than or equal to' (≤), shade below the line.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It represents all the points that satisfy all inequalities in the system.

Front

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

Back

The point (0, 0) is often tested to see if it is a solution to the system. If it satisfies all inequalities, it is part of the solution set.

Front

How can you tell 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 is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents all points below the line y = 2x + 3, with a dashed line indicating that points on the line are not included in the solution.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

It represents all points above the line y = 2x - 4, with a dashed line indicating that points on the line are not included in the solution.