Flashcard 4.3-4.4 Linear Inequalities and System of Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

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 inequalities in the system simultaneously.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

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 is the solution set of a system of inequalities?

Back

The solution set is the set of all points that satisfy all inequalities in the system, represented by the shaded region on the graph.

Front

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on a graph where all constraints (inequalities) are satisfied, representing all possible solutions.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities, which is crucial for finding solutions to systems of inequalities.

Front

How can you express a system of inequalities algebraically?

Back

A system of inequalities can be expressed as multiple inequalities, each representing a constraint on the variables.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line will be shaded.