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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Erica gets paid at home for doing extra chores. Last week, she did 22 loads of laundry and 88 loads of dishes, and her parents paid her $14\$14. The week before, she finished 11 load of laundry and 88 loads of dishes, earning a total of $11\$11. How much does Erica earn for completing each type of chore? Erica 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. Erica gets paid at home for doing extra chores. Last week, she did 22 loads of laundry and 88 loads of dishes, and her parents paid her $14\$14. The week before, she finished 11 load of laundry and 88 loads of dishes, earning a total of $11\$11. How much does Erica earn for completing each type of chore? Erica earns $____\$\_\_\_\_ per load of laundry and $____\$\_\_\_\_ per load of dishes.
  1. Define Earnings Equations: Let's denote the payment for a load of laundry as ll and for a load of dishes as dd. From the first week, Erica's earnings give us the equation 2l+8d=142l + 8d = 14.
  2. Use Elimination Method: From the previous week, the earnings equation is 1l+8d=111l + 8d = 11.
  3. Subtract Equations: We will use elimination to solve for one of the variables. Multiply the second equation by 22 to align the coefficients of ll in both equations: 2l+16d=222l + 16d = 22.
  4. Solve for d: Subtract the first equation from the modified second equation: \(2l + 1616d) - (22l + 88d) = 2222 - 1414\, which simplifies to (8\)d = 88\.
  5. Substitute dd into First Equation: Solving for dd, we get d=88d = \frac{8}{8}, which simplifies to d=1d = 1.
  6. Solve for ll: Substitute d=1d = 1 back into the first equation: 2l+8(1)=142l + 8(1) = 14, which simplifies to 2l+8=142l + 8 = 14.
  7. Solve for ll: Substitute d=1d = 1 back into the first equation: 2l+8(1)=142l + 8(1) = 14, which simplifies to 2l+8=142l + 8 = 14. Solving for ll, we get 2l=14−82l = 14 - 8, which simplifies to 2l=62l = 6. Then, l=62l = \frac{6}{2}, which simplifies to l=3l = 3.

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