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 $2$ loads of laundry and $8$ loads of dishes, and her parents paid her $\$14$ . The week before, she finished $1$ load of laundry and $8$ loads of dishes, earning a total of $\$11$ . 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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Solve a system of equations using elimination: word problems

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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

2

loads of laundry and

8

loads of dishes, and her parents paid her

\$14

. The week before, she finished

1

load of laundry and

8

loads of dishes, earning a total of

\$11

. How much does Erica earn for completing each type of chore? Erica earns

\$\_\_\_\_

per load of laundry and

\$\_\_\_\_

per load of dishes.

Define Earnings Equations: Let's denote the payment for a load of laundry as $l$ and for a load of dishes as $d$ . From the first week, Erica's earnings give us the equation $2l + 8d = 14$ .
Use Elimination Method: From the previous week, the earnings equation is $1l + 8d = 11$ .
Subtract Equations: We will use elimination to solve for one of the variables. Multiply the second equation by $2$ to align the coefficients of $l$ in both equations: $2l + 16d = 22$ .
Solve for d: Subtract the first equation from the modified second equation: $2l + $16$ d) - ( $2$ l + $8$ d) = $22$ - $14$ \, which simplifies to (8$d = $8$ \.
Substitute $d$ into First Equation: Solving for $d$ , we get $d = \frac{8}{8}$ , which simplifies to $d = 1$ .
Solve for $l$ : Substitute $d = 1$ back into the first equation: $2l + 8(1) = 14$ , which simplifies to $2l + 8 = 14$ .
Solve for $l$ : Substitute $d = 1$ back into the first equation: $2l + 8(1) = 14$ , which simplifies to $2l + 8 = 14$ . Solving for $l$ , we get $2l = 14 - 8$ , which simplifies to $2l = 6$ . Then, $l = \frac{6}{2}$ , which simplifies to $l = 3$ .