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The problem presents a shopping scenario with Ali, Badar, and Carli buying various items. We are asked to build a system of equations that models the purchases. The items bought include notebooks, pencils, and erasers. Let's define variables for the cost of each:

- Let \( x \) represent the cost of a notebook.
- Let \( y \) represent the cost of a pencil.
- Let \( z \) represent the cost of an eraser.

### From the given text:

1. **Ali's purchases:**
   - 2 notebooks, 1 pencil, 1 eraser
   - Total cost = Rp 4,700
   \[
   2x + y + z = 4700
   \]

2. **Badar's purchases:**
   - 1 notebook, 2 pencils, 1 eraser
   - Total cost = Rp 4,300
   \[
   x + 2y + z = 4300
   \]

3. **Carli's purchases:**
   - 3 notebooks, 2 pencils, 1 eraser
   - Total cost = Rp 7,100
   \[
   3x + 2y + z = 7100
   \]

Now, checking the options, we need to select the system of equations that matches the above information. Let's review the choices:

- The first option:
  \[
  2x + y + z = 4700 \\
  x + 2y + z = 4300 \\
  3x + 2y + z = 7100
  \]
  This option matches the correct system.

Thus, the correct answer is the **first option**.

Would you like more details or explanations?

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### Related Questions:
1. How can we solve this system of equations to find \( x \), \( y \), and \( z \)?
2. What method can be used to solve systems of equations like this (e.g., substitution or elimination)?
3. How would the system change if one of the item prices increased by a percentage?
4. How can you represent this system of equations graphically?
5. Can systems like these be solved using matrices?

### Tip:
When solving systems of equations, always check each equation for accuracy in representing the given problem before proceeding to solve!

Ali membeli dua buah buku tulis, sebuah pensil, dan sebuah penghapus seharga Rp 4.700. Badar membeli satu buku tulis, dua pensil, dan sebuah penghapus seharga Rp 4.300. Carli membeli tiga buku tulis, dua pensil, dan sebuah penghapus seharga Rp 7.100. Model matematika yang tepat untuk pernyataan ini adalah?

Learn how to solve a system of linear equations based on a shopping scenario where Ali, Badar, and Carli buy books, pencils, and erasers. This problem introduces key algebraic concepts like solving simultaneous equations. Suitable for students in Grades 7-9.

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