Graphing 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.

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What does it mean if two inequalities are parallel in a system?

Back

If two inequalities are parallel, it means they have the same slope but different y-intercepts. The solution may be empty, or it may include overlapping shaded regions.

Front

How do you graph an inequality with a 'greater than' symbol?

Back

To graph an inequality with a 'greater than' symbol, use a dashed line to indicate that points on the line are not included in the solution set, and shade the region above the line.

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 set (for 'greater than or equal to' or 'less than or equal to'), while a dashed line indicates that points on the line are not included (for 'greater than' or 'less than').

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

Front

What does the shaded region in a graph of inequalities represent?

Back

The shaded region represents all the possible solutions to the system of inequalities. Points within this region satisfy all inequalities.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection of shaded regions represents the set of solutions that satisfy all inequalities in the system.

Front

How can you identify the solution set of a system of inequalities graphically?

Back

The solution set can be identified by graphing each inequality, shading the appropriate regions, and finding the overlapping area where all shaded regions intersect.

Front

What is the role of the boundary line in graphing inequalities?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. The type of line (solid or dashed) indicates whether points on the line are included.

Front

What is an example of a system of inequalities?

Back

An example of a system of inequalities is: 1) y < 2x + 3 and 2) y ≥ -x + 1.