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Write a system of equations to describe the situation below, solve using elimination, 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 55 twin beds and 33 queen beds and used a total of 6262 pillows. At another house, she used 3434 pillows to spruce up 55 twin beds and 11 queen bed. 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 elimination, 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 55 twin beds and 33 queen beds and used a total of 6262 pillows. At another house, she used 3434 pillows to spruce up 55 twin beds and 11 queen bed. 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 xx be the number of pillows on every twin bed and yy be the number of pillows on every queen bed. We can write two equations based on the given information:\newlineFor the first house: 5x+3y=625x + 3y = 62 (Equation 11)\newlineFor the second house: 5x+1y=345x + 1y = 34 (Equation 22)\newlineWe will use these equations to solve for xx and yy using the elimination method.
  2. Elimination Method: To eliminate one of the variables, we can multiply Equation 22 by −3-3 so that when we add it to Equation 11, the yy terms will cancel out.\newline−3(5x+1y)=−3(34)-3(5x + 1y) = -3(34)\newline−15x−3y=−102-15x - 3y = -102 (Equation 33)
  3. Combine Equations: Now we add Equation 33 to Equation 11 to eliminate yy:$5x+3y\$5x + 3y + (−15-15x - 33y) = 6262 + (−102-102)\)This simplifies to:5x−15x+3y−3y=62−1025x - 15x + 3y - 3y = 62 - 102−10x=−40-10x = -40
  4. Solve for x: We can now solve for xx by dividing both sides of the equation by −10-10:\newline−10x/−10=−40/−10-10x / -10 = -40 / -10\newlinex=4x = 4\newlineSo the realtor used 44 pillows on every twin bed.
  5. Substitute xx into Equation: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. We'll use Equation 22:\newline5(4)+1y=345(4) + 1y = 34\newline20+y=3420 + y = 34
  6. Solve for y: Subtract 2020 from both sides of the equation to solve for y:\newline20+y−20=34−2020 + y - 20 = 34 - 20\newliney=14y = 14\newlineSo the realtor used 1414 pillows on every queen bed.

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