To model the situation with a system of equations, we need to consider the information provided:
- Jody earns $9 per hour babysitting and $10 per hour doing yard work.
- She worked a total of 34 hours.
- She earned a total of $410.
Let:
- \( x \) = number of hours babysitting
- \( y \) = number of hours doing yard work
From the information given, we can set up the following two equations:
-
The total hours worked equation: \[ x + y = 34 \]
-
The total earnings equation: \[ 9x + 10y = 410 \]
Thus, the system of equations that models this situation is:
\[ \begin{cases} x + y = 34 \ 9x + 10y = 410 \end{cases} \]