Graphing System 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 graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution set 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 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 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 the inequalities y > -4/5x - 1 and y ≤ 2/3x + 3?

Back

The solution set is the region above the line y = -4/5x - 1 and below or on the line y = 2/3x + 3.

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 does the term 'feasible region' refer to in the context of inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions to the system.

Front

What is the significance of the boundary lines in a system of inequalities?

Back

Boundary lines separate the different regions of the graph and indicate where the inequalities change from true to false.

Front

How do you match a system of inequalities to its graph?

Back

Identify the boundary lines and shading of the graph, then determine which inequalities correspond to those lines and shaded regions.

Front

What is an example of a system of inequalities?

Back

y < 2x + 1 and y ≥ -x - 3.