Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that involve 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 boundary line. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. Then shade the region that satisfies the inequality.

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 shaded region of the graph.

Front

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

Back

'≤' means 'less than or equal to' and includes the boundary line, while '<' means 'less than' and does not include the boundary line.

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. It is solid for '≤' or '≥' and dashed for '<' or '>'.

Front

How do you determine if a point is a solution to a linear 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, the point is a solution.

Front

What does the solution set of a system of linear inequalities represent?

Back

The solution set represents all possible combinations of values for the variables that satisfy all inequalities in the system.

Front

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

Back

The graph will have a dashed line for y = 2x - 4, and the region above the line will be shaded, indicating all points where y is greater than 2x - 4.

Front

What is the meaning of the inequality x + y ≤ 6 in a real-world context?

Back

This inequality could represent a constraint where the total number of two types of items (x and y) cannot exceed 6.

Front

How do you interpret the inequality 32x + 20y ≥ 150?

Back

This inequality indicates that the total number of cookies baked (32 chocolate chip cookies per hour and 20 snickerdoodle cookies per hour) must be at least 150.