systems of inequalities

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

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

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

Back

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

Front

What type of line is used to graph the inequality y < 2x + 3?

Back

A dotted line is used to graph y < 2x + 3 because the inequality does not include equality.

Front

What type of line is used to graph the inequality y ≥ -x + 1?

Back

A solid line is used to graph y ≥ -x + 1 because the inequality includes equality.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the region where all shaded areas overlap.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where all inequalities are satisfied, often represented as a shaded area.

Front

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

Back

If a point lies on the boundary line of an inequality, it is a solution if the inequality includes equality (e.g., ≤ or ≥).

Front

How can you check if a point is a solution to a specific inequality?

Back

Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.