https://file.aiquickdraw.com/mathbot/file/1728567160438ubcbl20j.jpg

Let's address the mathematical questions shown in the image one by one:

### Question 4:
**Find the solution set of the system of linear equations \(x + 2y = 4\) and \(2x + 4y = 12\) using graphical method.**

You have a system of two linear equations:
1. \(x + 2y = 4\)
2. \(2x + 4y = 12\)

Since the second equation is just a multiple of the first equation, these lines represent the same line. Thus, this system has **infinitely many solutions**, as both equations describe the same line.

### Question 5:
**The price of 3 pencils and 2 books is Rp5,100, while the price of 2 pencils and 4 books is Rp7,400. Write the mathematical model of the problem.**

Let:
- \(p\) be the price of a pencil.
- \(b\) be the price of a book.

We can form two equations:
1. \(3p + 2b = 5100\)
2. \(2p + 4b = 7400\)

### Question 6:
**Galih buys 2 books and 1 eraser for Rp7,300, while Rena buys 3 books and 3 erasers for Rp13,500.**
   - a) Write the mathematical model of the problem.
   - b) Find the price of a book and an eraser.

Let:
- \(b\) be the price of a book.
- \(e\) be the price of an eraser.

We form two equations:
1. \(2b + e = 7300\)
2. \(3b + 3e = 13500\)

We can solve these equations to find the prices.

### Question 7:
**The price of 3 thin notebooks and 2 thick notebooks is Rp15,500, while the price of 3 thin notebooks is Rp3,500 more expensive than 1 thick notebook. What is the price of a thin and a thick notebook?**

Let:
- \(t\) be the price of a thin notebook.
- \(T\) be the price of a thick notebook.

We have the system of equations:
1. \(3t + 2T = 15500\)
2. \(3t = T + 3500\)

### Question 8:
**The sum and difference of two numbers 12 and 4. Find:**
   - a) The mathematical model.
   - b) Each number.
   - c) The square of their difference.

Let:
- \(x = 12\)
- \(y = 4\)

We compute:
- Sum: \(x + y = 12 + 4 = 16\)
- Difference: \(x - y = 12 - 4 = 8\)
- The square of the difference: \((x - y)^2 = 8^2 = 64\)

Would you like to continue with more detailed solutions or explanations for each question? 

Here are 5 additional questions to consider:
1. How do you graphically solve a system of linear equations?
2. What strategies can help solve simultaneous equations involving prices?
3. Can you explain the logic behind creating equations for word problems?
4. How does identifying dependent and independent equations affect the solution set?
5. What is the significance of the sum and difference of squares in number theory?

**Tip:** When solving word problems, always assign variables to unknown quantities and form equations step by step.

Solve several math problems involving linear equations, simultaneous equations, and word problems about pricing, quantities, and basic operations.

Solve various math problems involving linear equations, simultaneous equations, and basic arithmetic word problems. Topics include solving for unknowns in pricing scenarios, finding solutions for systems of equations, and working with basic operations like addition, subtraction, and squaring differences. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation