System of Inequalities Review

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

What does the symbol '≤' represent in an inequality?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '>' represent in an inequality?

Back

'>' means 'greater than'. It indicates that the value on the left must be greater than the value on the right.

Front

What type of line is used to represent 'y < mx + b' on a graph?

Back

A dashed line is used to represent 'y < mx + b' because the points on the line are not included in the solution set.

Front

What type of line is used to represent 'y ≤ mx + b' on a graph?

Back

A solid line is used to represent 'y ≤ mx + b' because the points on the line are included in the solution set.

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

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 does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it is included in the solution set if the inequality is '≤' or '≥', but not if it is '<' or '>'.

Front

What is the graphical representation of the inequality 'y > 3x + 1'?

Back

The graphical representation is a dashed line for 'y = 3x + 1' with the area above the line shaded.

Front

What is the graphical representation of the inequality 'y ≤ -2x + 4'?

Back

The graphical representation is a solid line for 'y = -2x + 4' with the area below the line shaded.