Systems of Inequalities Test Recovery

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you determine 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 does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the shaded area indicates the solutions.

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

How do you graph the inequality y > 2x - 4?

Back

1. Graph the line y = 2x - 4 with a dashed line. 2. Shade the area above the line, as it represents all points where y is greater than 2x - 4.

Front

What does the solution set of a system of inequalities look like?

Back

The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap on the graph.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.

Front

How can you check if a point is not a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If it fails to satisfy any inequality, it is not a solution.

Front

What is the meaning of the term 'feasible region'?

Back

The feasible region is the area on a graph that represents all possible solutions to a system of inequalities.