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

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 a solid line represent in a graph of an inequality?

Back

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

Front

What does a dashed line represent in a graph of an inequality?

Back

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

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

How can you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use a solid or dashed line based on the inequality. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

Front

What does the inequality y ≤ 3x represent graphically?

Back

It represents all points below or on the line y = 3x, including the line itself.

Front

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

Back

It represents all points above the line y = -2x + 4, excluding the line itself.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the solution set from the non-solution set. Points on the line may or may not be included based on the type of inequality.

Front

How do you test a point to see if it is a solution to a system of inequalities?

Back

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