Graphs of 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 graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane. Use dashed lines for 'greater than' or 'less than' and solid lines for 'greater than or equal to' or 'less than or equal to'. The solution set is where the shaded regions overlap.

Front

What does the inequality y > 2x - 4 represent?

Back

It represents the region above the line y = 2x - 4, where y is greater than the value of 2x - 4.

Front

What does the inequality y < 2 represent?

Back

It represents the region below the horizontal line y = 2, where y is less than 2.

Front

What is the solution set of the system y > 2x - 4 and y < 2?

Back

The solution set is the area where the region above the line y = 2x - 4 overlaps with the region below the line y = 2.

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 it mean if a point is not part of the solution set?

Back

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

Front

What is the significance of dashed and solid lines in graphing inequalities?

Back

Dashed lines indicate that points on the line are not included in the solution (for < or >), while solid lines indicate that points on the line are included (for ≤ or ≥).

Front

How do you find the intersection of two inequalities?

Back

The intersection of two inequalities is found by identifying the region where the shaded areas of both inequalities overlap on the graph.

Front

What is the graphical representation of y ≤ 3x and y ≤ -2x + 4?

Back

The graphical representation includes the area below or on the line y = 3x and below or on the line y = -2x + 4.