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 point's coordinates 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, representing 'greater than or equal to' (≥) or 'less 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, representing 'greater than' (>) or 'less than' (<).

Front

What is the graphical representation of the inequality x > -3?

Back

The graph will have a dashed vertical line at x = -3, with shading to the right, indicating all values greater than -3.

Front

What is the boundary line in the inequality y ≤ 2x + 3?

Back

The boundary line is represented by the equation y = 2x + 3, and it is solid because the inequality includes 'less than or equal to' (≤).

Front

How do you graph the inequality y > -2x + 1?

Back

Graph the line y = -2x + 1 with a dashed line, then shade above the line to represent all points where y is greater than -2x + 1.

Front

What is the solution set of the system of inequalities y < 3 and y > x - 1?

Back

The solution set is the region where the area below the line y = 3 and above the line y = x - 1 overlap.

Front

What does the term 'feasible region' mean in the context of systems of inequalities?

Back

The feasible region is the area on the graph that satisfies all inequalities in the system, representing all possible solutions.

Front

How can you identify the correct graph for a given inequality?

Back

To identify the correct graph, check the slope and y-intercept of the line, the type of line (solid or dashed), and the direction of shading.