systems of inequalities

Front

What is a system of inequalities?

Back

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

Front

How do you represent a solution set graphically for a system of inequalities?

Back

The solution set is represented by the overlapping region of the graphs of the inequalities.

Front

What does a dotted line indicate when graphing an inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set, used for inequalities with < or >.

Front

What does a solid line indicate when graphing an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, used for inequalities with ≤ or ≥.

Front

How can 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 the significance of the boundary lines in a system of inequalities?

Back

Boundary lines separate the graph into regions, and the solution set is found in the region that satisfies all inequalities.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary, while a non-strict inequality (≤ or ≥) includes the boundary.

Front

How do you graph the inequality y ≤ (1/2)x + 2?

Back

Graph the line y = (1/2)x + 2 with a solid line, then shade below the line to represent y values that are less than or equal to the line.

Front

What is the solution set for the system of inequalities y ≤ (1/2)x + 2 and -y > -3x - 1?

Back

The solution set is the region where the shaded areas of both inequalities overlap.

Front

What does it mean if a point is not a solution to a system of inequalities?

Back

It means that the point does not satisfy at least one of the inequalities in the system.