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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTucker gets paid at home for doing extra chores. Last week, he did 66 loads of laundry and 88 loads of dishes, and his parents paid him $22\$22. The week before, he finished 66 loads of laundry and 44 loads of dishes, earning a total of $14\$14. How much does Tucker earn for completing each type of chore?\newlineTucker earns $____\$\_\_\_\_ per load of laundry and $____\$\_\_\_\_ per load of dishes.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTucker gets paid at home for doing extra chores. Last week, he did 66 loads of laundry and 88 loads of dishes, and his parents paid him $22\$22. The week before, he finished 66 loads of laundry and 44 loads of dishes, earning a total of $14\$14. How much does Tucker earn for completing each type of chore?\newlineTucker earns $____\$\_\_\_\_ per load of laundry and $____\$\_\_\_\_ per load of dishes.
  1. Define variables: Define the variables for the amount Tucker earns per load of laundry and per load of dishes.\newlineLet xx be the amount Tucker earns per load of laundry.\newlineLet yy be the amount Tucker earns per load of dishes.
  2. Write equations: Write the system of equations based on the given information.\newlineFrom the first week: 66 loads of laundry and 88 loads of dishes for $22\$22.\newline6x+8y=226x + 8y = 22\newlineFrom the week before: 66 loads of laundry and 44 loads of dishes for $14\$14.\newline6x+4y=146x + 4y = 14
  3. Use elimination: Use elimination to solve the system of equations.\newlineWe can eliminate xx by subtracting the second equation from the first equation.\newline(6x+8y)−(6x+4y)=22−14(6x + 8y) - (6x + 4y) = 22 - 14
  4. Perform subtraction: Perform the subtraction to find the value of yy.\newline6x+8y−6x−4y=22−146x + 8y - 6x - 4y = 22 - 14\newline8y−4y=88y - 4y = 8\newline4y=84y = 8\newliney=84y = \frac{8}{4}\newliney=2y = 2
  5. Substitute value: Substitute the value of yy into one of the original equations to solve for xx. Using the second equation: 6x+4(2)=146x + 4(2) = 14 6x+8=146x + 8 = 14 6x=14−86x = 14 - 8 6x=66x = 6 x=6/6x = 6 / 6 x=1x = 1
  6. Check solution: Check the solution by substituting both values into the other original equation.\newlineUsing the first equation: 6(1)+8(2)=226(1) + 8(2) = 22\newline6+16=226 + 16 = 22\newline22=2222 = 22\newlineThe solution checks out.

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