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 to the system is the set of all points that satisfy all inequalities in the system.

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 does it mean for a solution set to be represented graphically?

Back

A solution set represented graphically shows all the possible solutions to a system of inequalities on a coordinate plane, typically shaded regions that satisfy the inequalities.

Front

What is the significance of the boundary line in a graph of an inequality?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

Front

How can you represent a real-world situation as a system of inequalities?

Back

Identify the constraints and objectives of the situation, define variables for the quantities involved, and formulate inequalities based on those constraints.

Front

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

Back

The graphical representation is a region above the line y = 3x, which is dashed because the inequality is strict.

Front

What does the inequality 3b + 6t > 66 represent in a real-world context?

Back

It represents a constraint where the total earnings from babysitting (b) and tutoring (t) must be greater than $66.

Front

What is the maximum number of hours JoAnn can work at both jobs combined?

Back

JoAnn can work a maximum of 15 hours per week at both jobs combined, as represented by the inequality b + t < 15.

Front

How do you solve a system of inequalities graphically?

Back

To solve graphically, graph each inequality on the same coordinate plane, identify the feasible region where all shaded areas overlap, and that region represents the solution set.

Front

What is the meaning of the inequality x + y < 10 in a real-world scenario?

Back

It indicates that the total number of shots taken (x for 2-point shots and y for 3-point shots) must be less than 10.