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 points that satisfy all inequalities in the system.

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

Front

What does it mean to shade above a line in a graph?

Back

Shading above a line indicates that the solutions to the inequality are all the points above that line, meaning y-values are greater than the line's y-values.

Front

What does it mean to shade below a line in a graph?

Back

Shading below a line indicates that the solutions to the inequality are all the points below that line, meaning y-values are less than the line's y-values.

Front

What is the boundary line in a graph of inequalities?

Back

The boundary line is the line that separates the solutions from the non-solutions. It can be solid (for 'greater than or equal to' or 'less than or equal to') or dashed (for 'greater than' or 'less than').

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line represents that the points on the line are not included in the solution set, indicating 'greater than' or 'less than'.

Front

What does a solid line represent in graphing inequalities?

Back

A solid line represents that the points on the line are included in the solution set, indicating 'greater than or equal to' or 'less than or equal to'.

Front

How do you graph the inequality y > 2x + 3?

Back

To graph y > 2x + 3, first graph the line y = 2x + 3 as a dashed line, then shade above the line.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.