A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1500. The law firm assigned a total of 11 lawyers to the case and was able to charge the client $14100 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.

Let's define:

A = the number of associates assigned to the case.
P = the number of partners assigned to the case.

The law firm charges $700 per day for each associate, so the amount contributed by the associates to the total daily charge is 700A.
Similarly, the law firm charges $1500 per day for each partner, so the amount contributed by the partners to the total daily charge is 1500P.

According to the problem, the total daily charge for these lawyers' services is $14100. Hence, the equation can be written as:

700A + 1500P = 14100

This equation represents the total daily charge based on the number of associates and partners assigned to the case.

Let's denote the number of associates assigned to the case as 'A' and the number of partners assigned to the case as 'P'.

The system of equations can be written as follows:

Equation 1: A + P = 11 (The total number of lawyers assigned is 11)

Equation 2: 700A + 1500P = 14100 (The total daily rate charged for the lawyers' services is $14100)

Variables used:
A: Number of associates assigned to the case
P: Number of partners assigned to the case

a + p = 11

700a + 1500p = 14100