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, graph each inequality on the same coordinate plane. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. The solution set is the region where the shaded areas overlap.

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 overlapping 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 graph of inequalities?

Back

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

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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

The graphical representation is a dashed line for y = 3x, with the area above the line shaded, indicating all points where y is greater than 3x.

Front

What does the inequality 32x + 20y ≤ 150 represent in a real-world context?

Back

This inequality represents a constraint on the total number of cookies that can be baked, where x is the number of hours spent baking chocolate chip cookies and y is the number of hours spent baking snickerdoodle cookies.

Front

What is the meaning of the inequality x + y ≤ 6 in the context of baking cookies?

Back

This inequality indicates that the total hours spent baking chocolate chip cookies (x) and snickerdoodle cookies (y) cannot exceed 6 hours.

Front

How can you express the requirement of making at least 150 cookies using inequalities?

Back

The requirement can be expressed as 32x + 20y ≥ 150, meaning the total number of cookies made must be at least 150.