Understanding Systems of Inequalities

The video tutorial explains a system of linear inequalities modeling EDA's earnings from two part-time jobs. X represents hours babysitting at $8/hour, and Y represents hours scooping ice cream at $9/hour. The tutorial evaluates ordered pairs to determine viable solutions, ensuring they satisfy both inequalities: 8x + 9y > 105 and x + y < 13. The process involves checking each pair against the inequalities, eliminating non-viable options, and verifying the final solutions. The valid solutions are (2, 10) and (1, 11), which satisfy both conditions.

What do the variables X and Y represent in the context of EDA's jobs?

• X is the number of hours babysitting, Y is the number of hours worked scooping ice cream.

• X is the number of hours worked at a full-time job, Y is the number of hours at a part-time job.

• X is the number of hours worked scooping ice cream, Y is the number of hours babysitting.

• X is the total money earned, Y is the total hours worked.

Why is it important to consider the context when selecting viable solutions?

• Because the context determines the mathematical operations used.

• Because the context changes the inequality signs.

• Because the context helps in understanding the variables.

• Because the context ensures the solutions are realistic and applicable.

Which of the following ordered pairs is immediately eliminated by the inequality X + Y < 13?

• (2, 10)

• (12, 1)

• (1, 11)

• (8, 5)

What is the result of adding the hours in the pair (8, 5) and comparing it to 13?

• 13, which is equal to 13

• 13, which is less than 13

• 13, which is greater than 13

• 12, which is less than 13

Why is it necessary to check both inequalities in a system?

• To ensure the solution is mathematically correct.

• To verify that the solution satisfies all conditions of the problem.

• To find the maximum possible value of X and Y.

• To determine the range of possible solutions.

What is the result of the calculation 8x + 9y for the pair (2, 10)?

• 105, which is equal to 105

• 106, which is less than 105

• 106, which is equal to 105

• 106, which is greater than 105

Which of the following pairs satisfies both inequalities in the system?

• (0, 13)

• (12, 1)

• (8, 5)

• (2, 10)

What is the final conclusion about the pair (1, 11) in the context of the inequalities?

• It satisfies neither inequality.

• It satisfies both inequalities.

• It satisfies only the second inequality.

• It satisfies only the first inequality.

What is the significance of the inequality 8x + 9y > 105 in this context?

• It represents the minimum money EDA needs to earn.

• It represents the maximum hours allowed.

• It represents the total money earned.

• It represents the total hours worked.

Which of the following is a valid conclusion from the problem-solving process?

• Two pairs satisfy the system of inequalities.

• Only one pair satisfies the system of inequalities.

• All pairs satisfy the system of inequalities.

• No pairs satisfy the system of inequalities.