To determine which system of equations can be used to solve this problem, let's break it down:

1. Let x be the price of a regular ticket.
2. Let y be the price of a 3-D ticket.

The problem tells us:

• The 3-D ticket costs $2.00 more than the regular ticket. This gives us the relationship between the two prices:
  y = x + 2

• Oliver bought five regular tickets and four 3-D tickets, and the total cost was $89. This gives us another equation:
  5x + 4y = 89

Now, looking at the options:

A.

• x = y + 2
• 5x + 4y = 89
  This is incorrect because it incorrectly says the regular ticket costs $2.00 more than the 3-D ticket.

B.

• y = x + 2
• 4x + 5y = 89
  This is incorrect because the second equation should be 5x + 4y = 89 (Oliver bought 5 regular tickets and 4 3-D tickets, not 4 regular and 5 3-D).

C.

• x + y = 2
• 4x + 5y = 89
  This is incorrect because the first equation incorrectly says the sum of the two ticket prices is $2.00, which isn't true.

D.

• y = x + 2
• 5x + 4y = 89
  This is correct. It correctly states that the 3-D ticket is $2 more than the regular ticket and uses the right combination of tickets.

Thus, the correct answer is D.

Would you like more details on solving this system or any other questions?

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Here are 5 related questions:

1. How do you solve a system of equations using substitution?
2. How can you graphically represent the solution of a system of equations?
3. What happens if two equations in a system are parallel?
4. How do you solve a system of equations using the elimination method?
5. What is the difference between dependent, independent, and inconsistent systems of equations?

Tip: When solving a system of equations, always verify that both equations are consistent with the problem's conditions.