text: ## bprice26 3 years ago Auditions for a new, upcoming band in Chicago were held with 102 men and women trying out for the lead singer position. If twice the number of men less three times the number of women is equal to -6, how many women auditioned?
  
  1. PaxPolaris
  
  Using two variables let m be the number of men, ... & w the number of women $\Large m+w=102$ $\Large 2m-3w=-6$
  
  2. bprice26
  
  i already had an equation written out ; i just don't know what to do from there ..
  
  3. PaxPolaris
  
  multiply the first eq by 2
  
  4. PaxPolaris
  
  then subtract the second equation
  
  5. bprice26
  
  What ? How would i do that .. Do i multiply 102 by 2 ??? I am soooo confused , i have been reading all my lessons and doing all my work i just don't get it, it makes no sense to me ...
  
  6. PaxPolaris
  
  Well actually there are to methods, the use of simultaneous equations that i used above and using substitution...
  
  7. bprice26
  
  Okay well how does the substituion method work ?
  
  8. PaxPolaris
  
  *2 methods Using substitution: $\large m+w= 102$$\large \implies w=102-m$ put that in 2nd equation
  
  9. PaxPolaris
  
  $\large 2m-3\left( 102-m \right)=-6$
  
  10. bprice26
  
  Okay ; now i get it ! Thanks (:
  
  11. PaxPolaris
  
  $\large \implies 2m-306+3m=-6$$\large \implies 5m=306-6$$\large \implies 5m=300$
  
  12. PaxPolaris
  
  $\Large m=60$$\Large w={\large 102-60}=42$ Using simultaneous equations:$\large m+w=102$$\large \implies 2m+2w=204$ Subtracting the second equation:$\Large \begin{matrix}2m+2w=204 \\ 2m-3w=-6 \\ -\ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \\ \overline{\ \ \ \ \ \ \ \ \ \ 5w=210}\end{matrix}$
explanation: The document contains a math question and a detailed answer provided through a conversation between a user and a tutor. The question is about solving a system of linear equations to find the number of women who auditioned for a band. The answer is derived using both substitution and simultaneous equations methods.
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: ## bprice26 3 years ago Auditions for a new, upcoming band in Chicago were held with 102 men and women trying out for the lead singer position. If twice the number of men less three times the number of women is equal to -6, how many women auditioned?
  
  1. PaxPolaris
  
  Using two variables let m be the number of men, ... & w the number of women $\Large m+w=102$ $\Large 2m-3w=-6$
  
  2. bprice26
  
  i already had an equation written out ; i just don't know what to do from there ..
  
  3. PaxPolaris
  
  multiply the first eq by 2
  
  4. PaxPolaris
  
  then subtract the second equation
  
  5. bprice26
  
  What ? How would i do that .. Do i multiply 102 by 2 ??? I am soooo confused , i have been reading all my lessons and doing all my work i just don't get it, it makes no sense to me ...
  
  6. PaxPolaris
  
  Well actually there are to methods, the use of simultaneous equations that i used above and using substitution...
  
  7. bprice26
  
  Okay well how does the substituion method work ?
  
  8. PaxPolaris
  
  *2 methods Using substitution: $\large m+w= 102$$\large \implies w=102-m$ put that in 2nd equation
  
  9. PaxPolaris
  
  $\large 2m-3\left( 102-m \right)=-6$
  
  10. bprice26
  
  Okay ; now i get it ! Thanks (:
  
  11. PaxPolaris
  
  $\large \implies 2m-306+3m=-6$$\large \implies 5m=306-6$$\large \implies 5m=300$
  
  12. PaxPolaris
  
  $\Large m=60$$\Large w={\large 102-60}=42$ Using simultaneous equations:$\large m+w=102$$\large \implies 2m+2w=204$ Subtracting the second equation:$\Large \begin{matrix}2m+2w=204 \\ 2m-3w=-6 \\ -\ \ \ \ \ \ \ +\ \ \ \ \ \ \ \ +\ \ \ \ \ \ \\ \overline{\ \ \ \ \ \ \ \ \ \ 5w=210}\end{matrix}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed answer provided through a conversation between a user and a tutor. The question is about solving a system of linear equations to find the number of women who auditioned for a band. The answer is derived using both substitution and simultaneous equations methods.
  
  Label: question-and-answer