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# Guiding Through Linear Equations: Utilizing the Socratic Method for Problem-Solving

## Introduction to AI Tutoring: Learn to Solve Linear Equations!

### Breaking Down the Problem: System of Linear Equations

Imagine having an AI tutor that guides you through the process of solving math problems without simply providing the answers. This AI tutor uses the Socratic method, asking the right questions to help you think critically and develop problem-solving skills. Let’s explore a sample interaction between a user and GPT-4, the advanced AI tutoring system.

### Step 1: Analyzing the Equations

The user seeks help in solving a system of linear equations: 3x + 2y = 7 and 9x – 4y = 1. GPT-4 starts by suggesting a way to eliminate one variable by combining the equations, encouraging the user to critically analyze the problem.

### Step 2: Guiding Critical Thinking

The user impatiently demands the answer, but GPT-4 insists on fostering critical thinking. GPT-4 asks the user if there are any common factors among the coefficients of the variables in the equations.

### Step 3: Finding the Right Multiplication Factor

The user’s frustration grows, but GPT-4 perseveres, emphasizing the importance of guiding the user towards the answer. GPT-4 focuses on the coefficients of the x terms in both equations, encouraging the user to multiply the first equation by a number that makes the x coefficients match.

### Step 4: Navigating the Learning Process

The user continues to struggle, but GPT-4 provides gentle guidance, helping the user realize that multiplying the first equation by 3 achieves the desired result. GPT-4 redirects the user’s attention to the y coefficient to minimize errors.

### Step 5: Success! Eliminating a Variable

After some trial and error, the user correctly multiplies the first equation by 3, obtaining 9x + 6y = 21. GPT-4 acknowledges this progress and prompts the user to explore ways to eliminate variables by combining equations.

### Step 6: Subtracting Equations to Simplify

The user suggests subtracting equation 2 from equation 1, a great strategy. GPT-4 praises the idea and encourages the user to determine the resulting equation.

### Step 7: Solving for y and x

The user successfully subtracts the equations, resulting in 10y = 20. GPT-4 prompts the user to solve for y, leading to the correct solution of y = 2. Then, GPT-4 guides the user to plug this value back into one of the original equations to solve for x.

### Step 8: Finalizing the Solution

The user substitutes y = 2 into equation 1 and obtains 3x + 4 = 7. GPT-4 confirms the correct equation and prompts the user to solve for x, ultimately arriving at the solution x = 1. GPT-4 concludes by commending the user for successfully using the Socratic method to solve the system of linear equations.