Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

What does it mean for a point to be 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 shaded region of the graph.

Front

What is the perimeter of a rectangle?

Back

The perimeter of a rectangle is the total distance around the rectangle, calculated as P = 2(length + width).

Front

If the length of a rectangle is 3 times the width, how can you express the length in terms of the width?

Back

If w is the width, then the length l can be expressed as l = 3w.

Front

What is the area of a rectangle?

Back

The area of a rectangle is calculated as A = length × width.

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 significance of the boundary line in a system of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. It divides the graph into regions that satisfy or do not satisfy the inequality.

Front

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

Back

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

Front

What does the inequality 7.5x + 5.5y ≥ 2000 represent?

Back

It represents a condition where the total revenue from selling x adult tickets at $7.50 and y children's tickets at $5.50 must be at least $2000.