Solving Systems of Inequalities 2025

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 linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (<, >) or inclusive (≤, ≥). Then, shade the region that satisfies the inequality.

Front

What does the solution to a system of inequalities represent?

Back

The solution to a system of inequalities represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

Front

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

Back

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

Front

What does the inequality y ≥ -5/4 x + 3 represent?

Back

It represents all points (x, y) that lie on or above the line y = -5/4 x + 3.

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 is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. The line itself is included if the inequality is ≤ or ≥.

Front

How do you write a system of inequalities from a word problem?

Back

Identify the constraints and objectives in the problem, then express them as inequalities using variables to represent the quantities involved.

Front

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

Back

It 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

What is the meaning of the inequality 7.5x + 5.5y ≥ 2000?

Back

It indicates that the total revenue from selling x adult tickets at $7.50 and y children's tickets at $5.50 must be at least $2000.