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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution set is where the shaded regions overlap.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

What is the difference between '≤' and '<' in inequalities?

Back

'≤' means 'less than or equal to', including the boundary line, while '<' means 'less than', excluding the boundary line.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. It is included in the solution if the inequality is '≤' or '≥', but not if it is '<' or '>'.

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

The graph of y > 2x - 4 is a dashed line representing the equation y = 2x - 4, with the area above the line shaded.

Front

What does the inequality x + y ≤ 300 represent in a real-world context?

Back

This inequality represents a constraint where the total number of items (x and y) cannot exceed 300, such as the number of seats in a theater.

Front

How can you express a real-world scenario as a system of inequalities?

Back

Identify the constraints and conditions of the scenario, then translate them into inequalities using variables to represent the quantities involved.

Front

What is the solution set of the system: y ≤ 3x and y > -2x + 4?

Back

The solution set is the region where the area below the line y = 3x overlaps with the area above the line y = -2x + 4.