Rachel and Avery each opened up their own savings account on the same day. Rachel deposits 25 dollars into her account when she first opens it and decides to add 10 dollars each month. Avery deposits 20 dollars into his account when he first opens it and decides to add 9 dollars each month. Define the variables, create a system of linear equations, and use the system to determine when their bank accounts will have the same amount. Then explain the solution.

The time when they will have the same amount is -5 months or in the actual, they will have the same amount of 0 dollars on the day they opened their account (before they make deposits into the accounts)

Please see attached graph of the account balances

Step-by-step explanation:

The given information are;

The amount deposited by Rachel when she opened her account = 25 dollars

The amount Rachel deposits every month into her account = 10 dollars

The amount deposited by Avery when she opened her account = 20 dollars

The amount Avery deposits every month into her account = 9 dollars

The amount, y in Rachel's account after x month is therefore;

y = 25 + 10×x

The amount, z in Avery's account after x month is given also as follows;

z = 20 + 9×x

The bank accounts will have the same amount when the y = z, therefore, at the time when the amounts in the accounts are equal, we have;

25 + 10×x = 20 + 9×x

25 - 20 =9×x - 10×x

5 = -x

x = -5

The time when they will have the same amount is -5 months or in the actual, they will have the same amount of 0 dollars on the day they opened their account (before they make deposits into the accounts).