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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAubrey is a salon owner. Yesterday, she did 55 haircuts and colored the hair of 11 client, charging a total of $338\$338. Today, she did 44 haircuts and colored the hair of 11 client, charging a total of $289\$289. How much does Aubrey charge for her services?\newlineAubrey charges $_\$\_ for a haircut and $_\$\_ for a coloring.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAubrey is a salon owner. Yesterday, she did 55 haircuts and colored the hair of 11 client, charging a total of $338\$338. Today, she did 44 haircuts and colored the hair of 11 client, charging a total of $289\$289. How much does Aubrey charge for her services?\newlineAubrey charges $_\$\_ for a haircut and $_\$\_ for a coloring.
  1. Define variables: Let's define two variables: let xx be the cost of a haircut, and yy be the cost of coloring. We can write two equations based on the given information.\newlineFrom the first day: 5x+y=3385x + y = 338 (Equation 11)\newlineFrom the second day: 4x+y=2894x + y = 289 (Equation 22)\newlineWe will use these equations to solve for xx and yy using the elimination method.
  2. Elimination method: To eliminate yy, we can subtract Equation 22 from Equation 11.(5x+y)−(4x+y)=338−289(5x + y) - (4x + y) = 338 - 289This simplifies to:5x−4x+y−y=338−2895x - 4x + y - y = 338 - 289
  3. Calculate cost of haircut: Simplifying the equation further, we get:\newlinex=338−289x = 338 - 289\newlinex=49x = 49\newlineSo, Aubrey charges $49\$49 for a haircut.
  4. Substitute value of x: Now that we have the value for xx, we can substitute it back into either Equation 11 or Equation 22 to find the value of yy. Let's use Equation 22.4(49)+y=2894(49) + y = 289196+y=289196 + y = 289
  5. Calculate cost of coloring: Subtract 196196 from both sides to solve for yy: \newliney=289−196y = 289 - 196\newliney=93y = 93\newlineSo, Aubrey charges $93\$93 for coloring.

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