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The problem presents a situation where Charles has 13 coins (a mix of pennies and dimes) worth $0.58. The task asks to represent this situation with a system of equations, where $x$ represents the number of pennies and $y$ represents the number of dimes.

### Step-by-step:
1. **Total number of coins**: The total number of pennies and dimes is 13.
   \[
   x + y = 13
   \]
   (This represents that the total number of coins is the sum of pennies and dimes.)

2. **Total value of coins**: Pennies are worth $0.01 each, and dimes are worth $0.10 each. The total value of Charles' collection is $0.58.
   \[
   0.01x + 0.10y = 0.58
   \]
   (This represents the total value in terms of the number of pennies and dimes.)

### System of equations:
\[
\begin{aligned}
x + y &= 13 \\
0.01x + 0.10y &= 0.58
\end{aligned}
\]

This is the system of equations that represents the problem.

Let me know if you'd like help with solving this system of equations or more details on forming an augmented matrix!

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### Follow-up questions:
1. How do you solve this system of equations using substitution or elimination?
2. What would the augmented matrix look like for this system of equations?
3. What is the value of $x$ and $y$ after solving the system?
4. How do you interpret the meaning of the solution in the context of the problem?
5. What would change in the system if Charles had 14 coins instead of 13?

### Tip:
When setting up systems of equations, always check the units and what each variable represents to ensure accuracy.

Charles has a collection of pennies and dimes worth $0.58. He has 13 coins. Let x and y represent the numbers of pennies and dimes, respectively. Write a system of equations that can represent this situation.

Learn how to solve a system of equations involving pennies and dimes where the total coin count is 13, and the total value is $0.58. This example explains how to form and solve linear equations for Grade 7-9 students.

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