2,9 systems of linear inequalities word problems

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more 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 represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints (inequalities), and express the objective (goal) as an inequality.

Front

What does the inequality 2x + 3y > 100 represent in a word problem context?

Back

It indicates that the total value of items (where x and y are quantities of different items) must exceed $100.

Front

What does the inequality x + y ≤ 40 signify in a jewelry-making scenario?

Back

It signifies that the total number of jewelry pieces made (bracelets and earrings) cannot exceed 40.

Front

In the context of saving money, what does the inequality 8x + 25y ≥ 100 mean?

Back

It means that the total earnings from two jobs (x hours at $8/hour and y hours at $25/hour) must be at least $100.

Front

What is the significance of the maximum hours constraint in a work problem?

Back

It limits the total time available for work, ensuring that the sum of hours worked does not exceed the specified maximum.

Front

How do you interpret the inequality b + t < 15 in a babysitting and tutoring scenario?

Back

It indicates that the total hours spent babysitting (b) and tutoring (t) must be less than 15 hours.

Front

What does the inequality 3b + 6t > 66 represent in terms of earnings?

Back

It represents that the total earnings from babysitting (b at $3/hour) and tutoring (t at $6/hour) must exceed $66.

Front

What is the role of the graph in solving systems of inequalities?

Back

The graph visually represents the solution set of the inequalities, showing the feasible region where all conditions are satisfied.

Front

How do you determine the feasible region for a system of inequalities?

Back

By graphing each inequality on the same coordinate plane and identifying the overlapping area that satisfies all inequalities.