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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineNorma is a hairdresser. Before her lunch break, she gave 11 haircut and colored the hair of 11 client in 106106 minutes. After lunch, she gave 11 haircut and colored the hair of 44 clients in 346346 minutes. How long does it take for Norma to perform each type of service, assuming the amount of time doesn't vary from client to client?\newlineIt takes Norma _\_ minutes to give a haircut and _\_ minutes to color a client's hair.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineNorma is a hairdresser. Before her lunch break, she gave 11 haircut and colored the hair of 11 client in 106106 minutes. After lunch, she gave 11 haircut and colored the hair of 44 clients in 346346 minutes. How long does it take for Norma to perform each type of service, assuming the amount of time doesn't vary from client to client?\newlineIt takes Norma _\_ minutes to give a haircut and _\_ minutes to color a client's hair.
  1. Define variables for services: Step 11: Define the variables for the services Norma provides.\newlineLet xx be the time for a haircut and yy be the time to color a client's hair.
  2. Write equations based on information: Step 22: Write the equations based on the given information.\newlineFirst scenario: 11 haircut + 11 coloring = 106106 minutes.\newlinex+y=106x + y = 106\newlineSecond scenario: 11 haircut + 44 colorings = 346346 minutes.\newlinex+4y=346x + 4y = 346
  3. Choose variable to eliminate: Step 33: Choose the variable to eliminate using the elimination method.\newlineWe will eliminate xx by subtracting the first equation from the second.
  4. Perform subtraction to eliminate xx: Step 44: Perform the subtraction to eliminate xx.(x+4y)−(x+y)=346−106(x + 4y) - (x + y) = 346 - 106x+4y−x−y=346−106x + 4y - x - y = 346 - 1063y=2403y = 240
  5. Solve for y: Step 55: Solve for y.\newline3y=2403y = 240\newliney=2403y = \frac{240}{3}\newliney=80y = 80
  6. Substitute value of yy to find xx: Step 66: Substitute the value of yy back into the first equation to find xx.x+80=106x + 80 = 106x=106−80x = 106 - 80x=26x = 26

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