Question

Four friends are working to solve the system of inequalities y>5x and x≥9. Izabella substitutes 9 for x and then concludes that y≥45, but her friends disagree. Each friend presents an argument to explain his or her reasoning.

Part A: Whose argument is correct?
Part B: What is the correct solution?
Select one answer for Part A and one answer for Part B.
A: Ellis argues that because a solution must satisfy both equations, Izabella’s conclusion is incorrect. For example, if x=9, y must be greater than 5x, or 45. Thus, y≥45 cannot be the solution.
A: Maud argues that Izabella made a mistake in her substitution. She should have substituted 9 for y. This would give her 95>x. Thus, y≥45 cannot be the solution.
B: y≥45A: Izabella’s argument is, in fact, correct.B: x<95
A: Greyson argues that substitution is not a valid solution method for this problem. He claims that the only way to solve this problem is to graph it. Thus, y≥45 cannot be the solution.
B: y>45B: The solution cannot be determined.

Answer 1

Ellis's argument is correct and the correct solution is y>45.

Step-by-step explanation:

Part A: Ellis's argument is correct. In order for a solution to satisfy both inequalities, y must be greater than 5x and x must be greater than or equal to 9. Izabella's conclusion of y≥45 is incorrect because for x=9, y would have to be greater than or equal to 45, not just greater.

Part B: The correct solution is y>45. Since Izabella's conclusion of y≥45 is incorrect, we know that y must be strictly greater than 45, which is represented by y>45.