Graphing Systems of Inequalities Review

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is 'greater than or equal to' or 'less than or equal to').

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is 'greater than' or 'less than').

Front

How do 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 is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where all inequalities overlap, representing all possible solutions.

Front

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

Back

It represents the area above the line y = 2x - 4, not including the line itself.

Front

What does the inequality y < 2 represent graphically?

Back

It represents the area below the horizontal line y = 2, including the line itself.

Front

How do you graph the inequality y ≤ 3x + 1?

Back

Graph the line y = 3x + 1 as a solid line and shade below the line to represent all points where y is less than or equal to 3x + 1.

Front

What is the first step in solving a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane.

Front

What is the significance of the point (0,0) in a system of inequalities?

Back

(0,0) is often tested to see if it is a solution to the system; if it satisfies all inequalities, it is part of the solution set.

Front

How can you tell if a point is NOT part of the solution set?

Back

If substituting the point into any inequality results in a false statement, then it is not part of the solution set.