Checking Solutions of Two-Variable Inequalities

The video tutorial explores whether the point (2, 5) is a solution to a given system of inequalities. The system includes two inequalities: Y is greater than or equal to 2x plus 1, and X is greater than 1. The tutorial demonstrates that the point satisfies both inequalities, confirming it as a solution. The process involves substituting the values of X and Y into each inequality and verifying their truth. The tutorial concludes that (2, 5) meets the conditions of the system.

What are the two inequalities in the given system?

• Y is greater than or equal to 2x plus 1 and X is greater than 1

• Y is less than or equal to 2x plus 1 and X is less than 1

• Y is greater than 2x plus 1 and X is less than 1

• Y is less than 2x plus 1 and X is greater than 1

What must be true for (2, 5) to be a solution to the system?

• It must satisfy at least one inequality

• It must satisfy neither inequality

• It must satisfy both inequalities

• It must satisfy only one of the inequalities

What is the result of substituting X = 2 and Y = 5 into the first inequality?

• 5 is less than 5

• 5 is less than or equal to 5

• 5 is greater than or equal to 5

• 5 is greater than or equal to 4

Why does the first inequality hold true for (2, 5)?

• Because 5 is greater than 4

• Because 5 is equal to 5

• Because 5 is less than 5

• Because 5 is less than or equal to 4

Does (2, 5) satisfy the second inequality X > 1?

• Yes, because 2 is equal to 1

• No, because 2 is not greater than 1

• No, because 2 is less than 1

• Yes, because 2 is greater than 1