https://file.aiquickdraw.com/mathbot/file/1726792394939mgo8epq8.jpg

Looking at the image, it seems you're working with systems of linear equations. Let's go over the relevant questions:

### Problem Breakdown (Question 17):
You are asked which system of linear equations represents the given situation:
- **Juana** has 2 apples and 3 oranges costing **₱105**.
- Her friend has 1 apple and 4 oranges costing **₱90**.

Let:
- **x** = cost of one apple.
- **y** = cost of one orange.

We can form the following system of equations:
1. \( 2x + 3y = 105 \) (for Juana)
2. \( x + 4y = 90 \) (for her friend)

Thus, the correct system of equations is the one labeled as **C**.

### Correct Answer:
- **For question 17, the answer is C.**

### Question 18:
You are asked for the best first step to solve this system of equations:
- \( 2x + 3y = 105 \)
- \( x + 4y = 90 \)

The best first step is to multiply the second equation by 2, so that the coefficients of \( x \) in both equations become the same. After that, you can subtract the equations to eliminate \( x \) and solve for \( y \).

Thus, the correct answer to question 18 is **B** (Multiply equation 2 by 2).

Would you like further details or explanations on solving these systems?

### Expanding Questions:
1. How can you solve the system of equations after multiplying the second equation by 2?
2. What is the final value of \( x \) and \( y \) after solving this system?
3. Can substitution be an alternative method to solve this system? How?
4. What are the advantages of using elimination vs. substitution methods for solving systems of equations?
5. Can you graphically interpret the solution of this system of equations?

### Tip:
Always check if multiplying one equation by a constant can help align terms for easier elimination.

Which of the following systems of linear equations represents the situation (17) and what is the best step to solve it (18)?

Learn how to solve a system of linear equations based on the cost of apples and oranges. This detailed explanation covers key algebraic concepts using the elimination method, suitable for Grades 7-9.

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