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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineA realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 33 twin beds and 22 queen beds and used a total of 3434 pillows. At another house, she used 4646 pillows to spruce up 55 twin beds and 22 queen beds. How many decorative pillows did the realtor arrange on each bed?\newlineThe realtor used ____\_\_\_\_ pillows on every twin bed and ____\_\_\_\_ pillows on every queen bed.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineA realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 33 twin beds and 22 queen beds and used a total of 3434 pillows. At another house, she used 4646 pillows to spruce up 55 twin beds and 22 queen beds. How many decorative pillows did the realtor arrange on each bed?\newlineThe realtor used ____\_\_\_\_ pillows on every twin bed and ____\_\_\_\_ pillows on every queen bed.
  1. Define variables: Let's define the variables. Let xx be the number of pillows on each twin bed and yy be the number of pillows on each queen bed.
  2. Write first equation: Based on the information given for the first house, we can write the first equation as 3x+2y=343x + 2y = 34, where 33 is the number of twin beds and 22 is the number of queen beds.
  3. Write second equation: For the second house, the information given allows us to write the second equation as 5x+2y=465x + 2y = 46, where 55 is the number of twin beds and 22 is the number of queen beds.
  4. Solve using elimination: We now have a system of equations:\newline11) 3x+2y=343x + 2y = 34\newline22) 5x+2y=465x + 2y = 46\newlineWe can solve this system using the method of elimination or substitution. Let's use elimination to solve for xx and yy.
  5. Eliminate y: To eliminate y, we can subtract the first equation from the second equation:\newline(5x+2y)−(3x+2y)=46−34(5x + 2y) - (3x + 2y) = 46 - 34\newline5x+2y−3x−2y=125x + 2y - 3x - 2y = 12\newline2x=122x = 12\newlinex=122x = \frac{12}{2}\newlinex=6x = 6
  6. Substitute xx: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. Let's use the first equation:\newline3x+2y=343x + 2y = 34\newline3(6)+2y=343(6) + 2y = 34\newline18+2y=3418 + 2y = 34\newline2y=34−182y = 34 - 18\newline2y=162y = 16\newliney=162y = \frac{16}{2}\newliney=8y = 8

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