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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineEli gets paid at home for doing extra chores. Last week, he did 88 loads of laundry and 33 loads of dishes, and his parents paid him $35\$35. The week before, he finished 88 loads of laundry and 66 loads of dishes, earning a total of $38\$38. How much does Eli earn for completing each type of chore?\newlineEli 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.\newlineEli gets paid at home for doing extra chores. Last week, he did 88 loads of laundry and 33 loads of dishes, and his parents paid him $35\$35. The week before, he finished 88 loads of laundry and 66 loads of dishes, earning a total of $38\$38. How much does Eli earn for completing each type of chore?\newlineEli earns $\$_____ per load of laundry and $\$_____ per load of dishes.
  1. Define Variables: Let's denote the price per load of laundry as ll and the price per load of dishes as dd. Eli's earnings for 88 loads of laundry and 33 loads of dishes are $35\$35, leading to the equation 8l+3d=358l + 3d = 35.
  2. Set Up Equations: From the previous week, Eli did 88 loads of laundry and 66 loads of dishes for $38\$38, giving us the equation 8l+6d=388l + 6d = 38.
  3. Eliminate Variable: To eliminate one variable, we'll focus on eliminating ll. Multiply the first equation by −1-1 to align the coefficients of ll for subtraction. −8l−3d=−35-8l - 3d = -35.
  4. Solve for dd: Add this equation to the second equation: −8l−3d+8l+6d=−35+38-8l - 3d + 8l + 6d = -35 + 38, simplifying to 3d=33d = 3.
  5. Substitute and Simplify: Solve for dd: d=33d = \frac{3}{3}, which simplifies to d=1d = 1.
  6. Solve for ll: Substitute d=1d = 1 back into the first equation: 8l+3(1)=358l + 3(1) = 35. Simplify to 8l+3=358l + 3 = 35.
  7. Solve for ll: Substitute d=1d = 1 back into the first equation: 8l+3(1)=358l + 3(1) = 35. Simplify to 8l+3=358l + 3 = 35. Solve for ll: 8l=35−38l = 35 - 3, which simplifies to 8l=328l = 32. Then, l=328l = \frac{32}{8}, which simplifies to l=4l = 4.

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