Graphing 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 ordered pairs that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does it mean if a point is 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, meaning it lies in the overlapping shaded region of the graph.

Front

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

Back

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

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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the inequality x > -3 represent on a graph?

Back

The inequality x > -3 represents all points to the right of the vertical line x = -3, not including the line itself.

Front

What is the solution set of the inequalities -4y < 8 and 6x + 3 > 1?

Back

The solution set includes all ordered pairs (x, y) that satisfy both inequalities, such as (2, 3).

Front

Which of the following points is NOT a solution to the system of inequalities: (0, -1), (0, 3), (4, 0), (6, -2)?

Back

(0, -1) is NOT a solution to the system of inequalities.

Front

What is the graphical representation of the inequality y < 2x + 1?

Back

The graphical representation is a dashed line for the equation y = 2x + 1, with the area below the line shaded.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and the direction of shading. Use the appropriate inequality symbol based on whether the line is solid or dashed.