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

What does a dotted line represent in a graph of linear inequalities?

Back

A dotted line represents inequalities that are strict, such as < or >, indicating that points on the line are not included in the solution set.

Front

What does a solid line represent in a graph of linear inequalities?

Back

A solid line represents inequalities that are inclusive, such as ≤ or ≥, indicating that points on the line are included in the solution set.

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How do you determine if a point is a solution to a system of linear 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 graphical representation of the inequality y > x - 2?

Back

The graphical representation is a region above the line y = x - 2, with a dotted line indicating that points on the line are not included.

Front

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

Back

The graphical representation is a region below or on the line y = x + 3, with a solid line indicating that points on the line are included.

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, representing all possible solutions.

Front

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

Back

If a point lies on the boundary line, it may or may not be a solution, depending on whether the inequality is strict or inclusive.

Front

How can you graph a system of linear inequalities?

Back

To graph a system, first graph each inequality as a line (dotted or solid), then shade the appropriate region for each inequality, and identify the overlapping region.

Front

What is the significance of the intersection of shaded regions in a graph of linear inequalities?

Back

The intersection of shaded regions represents the set of all points that satisfy all inequalities in the system, which is the solution set.