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The problem is asking to choose the equations that represent a system of equations describing Polly's work at the movie theatre and babysitting. Let's break it down:

1. **Let $ x $ be the number of hours Polly worked at the movie theatre** and **$ y $ be the number of hours she babysat**.
2. Polly earns **$9.50 per hour at the movie theatre** and **$10 per hour babysitting**.
3. Polly worked a total of **20 hours last week** and earned **$194**.

From this, we can set up two equations:

- One equation for the **total hours worked**:  
  $ x + y = 20 $
  
- Another equation for the **total money earned**:  
  $ 9.50x + 10y = 194 $

### Now, let's analyze the provided options:
1. **$ 9.5x + 10y = 20 $** → Incorrect, because the total hours worked should equal 20, not the total money earned.
2. **$ y = 9.5x + 20 $** → Incorrect, because this does not represent the situation correctly (mixes hours with money).
3. **$ x + y = 20 $** → Correct, this represents the total hours worked.
4. **$ 9.5x + 10y = 194 $** → Correct, this represents the total money earned.
5. **$ y = 10x + 194 $** → Incorrect, does not match the situation.
6. **$ x + y = 194 $** → Incorrect, because the total money earned is 194, not the total hours.

### Correct answers:
- $ x + y = 20 $
- $ 9.5x + 10y = 194 $

Let me know if you want further clarification or have questions!

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Here are 5 related questions:
1. How would the equations change if Polly worked 25 hours in total?
2. If Polly earned $11 per hour babysitting instead of $10, how would you modify the system of equations?
3. How can we solve the system of equations using substitution?
4. What is the graphical interpretation of these equations?
5. How can we check if a solution to this system is correct?

**Tip:** When writing systems of equations, always align variables to represent the same type of quantity—like hours or dollars, not a mix.

Choose the equations that you could use to write and solve a system for the situation. Let x be the number of hours working at the movie theatre and y be the number of hours babysitting. Polly made $9.50 an hour working at the movie theatre and $10 an hour babysitting. She spent 20 hours working last week and made $194.

Learn how to solve a system of equations where Polly works at two different jobs: earning $9.50 per hour at a movie theater and $10 per hour babysitting. This problem explores total hours worked and total earnings, using algebraic methods to find the solution.

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