Systems of Inequalities

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 has 'or equal to' in it.

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 does not have 'or equal to' in it.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

A point is a solution if it satisfies all inequalities in the system.

Front

What is the standard form of a linear inequality?

Back

The standard form is typically written as Ax + By <, >, ≤, or ≥ C, where A, B, and C are constants.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid or dashed). 2. Choose a test point not on the line to determine which side of the line to shade.

Front

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

Back

The boundary line divides the coordinate plane into regions, each representing possible solutions to the inequalities.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be equal to the boundary.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than', indicating that the value cannot be equal to the boundary.

Front

If a manager needs more than $21,000 in revenue, how would you express this as an inequality?

Back

The inequality would be expressed as 225x + 175y > 21,000.

Front

Are the points on the boundary line part of the solution set for '≥' or '≤' inequalities?

Back

Yes, the points on the boundary line are part of the solution set for '≥' or '≤' inequalities.