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 linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the inequality 2x + 3y > 100 represent in a real-world context?

Back

It represents a situation where the total value of items (e.g., bracelets and earrings) sold must exceed $100.

Front

What is the meaning of the solution (1, 0) in the context of a system of inequalities?

Back

The point (1, 0) indicates that selling 1 bracelet and 0 earrings satisfies the conditions set by the inequalities.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

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 all inequalities are satisfied, the point is a solution.

Front

What is the significance of the maximum number of pieces of jewelry (x + y ≤ 40)?

Back

This inequality indicates that the total number of bracelets (x) and earrings (y) sold cannot exceed 40.

Front

What does the inequality 3b + 6t > 66 represent for JoAnn's job situation?

Back

It represents the condition that JoAnn's total earnings from babysitting (b) and tutoring (t) must be greater than $66.

Front

What is the role of the inequality b + t < 15 in JoAnn's job scenario?

Back

This inequality limits the total hours JoAnn can work to less than 15 hours per week.

Front

What is a feasible region in the context of systems of inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.