https://file.aiquickdraw.com/mathbot/file/17292772168108y97wppk.jpg

Let's go through the problem step by step.

### Part (a) - System of Equations:

We are given two scenarios:
1. You ordered 2 drink refills and an egg breakfast, totaling $8.40.
2. Your friend ordered 3 drink refills and an egg breakfast, totaling $9.35.

Let:
- $ r $ represent the cost of one refill.
- $ b $ represent the cost of the egg breakfast.

We can set up the system of equations based on these conditions:
1. $ 2r + b = 8.40 $ (for your order)
2. $ 3r + b = 9.35 $ (for your friend's order)

### Part (b) - Graphing the Equations:

To graph the equations, rewrite them in terms of $ b $ (egg breakfast price):

1. From the first equation:  
   $ b = 8.40 - 2r $
   
2. From the second equation:  
   $ b = 9.35 - 3r $

These equations represent two straight lines on a graph where:
- The x-axis is for $ r $ (the price of a refill).
- The y-axis is for $ b $ (the price of the egg breakfast).

The point where these lines intersect will give the values of $ r $ and $ b $.

### Part (c) - Estimate Costs from the Graph:

By plotting these two lines on a graph, the intersection point will estimate the cost of each item. The x-coordinate will give the value of $ r $ (refill price) and the y-coordinate will give $ b $ (egg breakfast price).

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Would you like me to help you plot the graph or solve the system of equations algebraically? Also, feel free to ask questions or request details!

Here are five related questions to expand on the topic:
1. How would you solve the system using substitution or elimination methods instead of graphing?
2. How do you check if the solution from the graph is accurate?
3. What other methods could be used to solve this system if graphing tools are unavailable?
4. How would the equations change if one person ordered two egg breakfasts instead?
5. Can you identify real-world situations where systems of equations like these are useful?

**Tip:** Always verify your solution by substituting the values of $ r $ and $ b $ back into the original equations to check their accuracy.

The restaurant bill you and your friend received was not itemized. You ordered 2 drink refills and the egg breakfast, for a total of $8.40. Your friend ordered 3 refills and the egg breakfast for $9.35.

Learn how to set up and solve a system of equations based on a restaurant bill. The problem involves two equations: one person orders 2 drink refills and an egg breakfast for $8.40, while their friend orders 3 refills and an egg breakfast for $9.35. This problem teaches algebraic concepts, graphing techniques, and solving systems of equations. Suitable for Grades 8-10.

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