System 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

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the region defined by those inequalities.

Front

How can 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 is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane that is either shaded above or below the line, depending on the inequality sign (greater than or less than).

Front

What is the difference between a solid line and a dashed line in the graph of an inequality?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

What does the term 'feasible region' refer to in the context of linear inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system overlap, representing all possible solutions.

Front

How do you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, graph each inequality as a line (solid or dashed) and shade the appropriate half-plane. The solution is where the shaded areas overlap.

Front

What is the significance of the vertices of the feasible region?

Back

The vertices of the feasible region are important because they are potential solutions to the system of inequalities and can be used to find optimal solutions in linear programming.

Front

What is an example of a linear inequality?

Back

An example of a linear inequality is y < 2x + 3, which represents all points below the line y = 2x + 3.

Front

What does it mean for a point to be 'not a solution' to a system of inequalities?

Back

A point is 'not a solution' if it does not satisfy at least one of the inequalities in the system, meaning it lies outside the feasible region.