text: # How do you solve the following system?:  3x-2y=4 , x-4y=3
  
  Nov 19, 2015
  
  I found:
  $x = 1$
  $y = - \frac{1}{2}$
  
  #### Explanation:
  
  We can isolate $x$ from the second equation and substitute into the first to find $y$:
  $x = 4 y + 3$
  Into the first:
  $3 \left(\textcolor{red}{4 y + 3}\right) - 2 y = 4$
  $12 y + 9 - 2 y = 4$
  $10 y = - 5$
  $y = - \frac{5}{10} = - \frac{1}{2}$
  Use this value back into:
  $x = 4 \left(\textcolor{red}{- \frac{1}{2}}\right) + 3 = - 2 + 3 = 1$
explanation: The document contains a math question and its corresponding answer. The question asks how to solve a system of linear equations, and the answer provides the solution for the variables \( x \) and \( y \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # How do you solve the following system?:  3x-2y=4 , x-4y=3
  
  Nov 19, 2015
  
  I found:
  $x = 1$
  $y = - \frac{1}{2}$
  
  #### Explanation:
  
  We can isolate $x$ from the second equation and substitute into the first to find $y$:
  $x = 4 y + 3$
  Into the first:
  $3 \left(\textcolor{red}{4 y + 3}\right) - 2 y = 4$
  $12 y + 9 - 2 y = 4$
  $10 y = - 5$
  $y = - \frac{5}{10} = - \frac{1}{2}$
  Use this value back into:
  $x = 4 \left(\textcolor{red}{- \frac{1}{2}}\right) + 3 = - 2 + 3 = 1$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks how to solve a system of linear equations, and the answer provides the solution for the variables \( x \) and \( y \).
  
  Label: question-and-answer