Answer:
To solve the system of equations graphically, we can start by defining our variables. Let x represent the number of associates assigned to the case, and let y represent the number of partners assigned to the case.
Given the daily rates for associates and partners, we can write the following equations to represent the cost per day for the lawyers' services:
Cost of associates per day = 400x
Cost of partners per day = 1200y
Since there are a total of 5 lawyers assigned to the case, we know that:
x + y = 5
We also know that the law firm charged the client $3600 per day for these lawyers' services, so we can write:
400x + 1200y = 3600
To graphically solve this system of equations, we can start by rearranging the equations in slope-intercept form:
400x + 1200y = 3600
1200y = -400x + 3600
y = (-1/3)x + 3
x + y = 5
y = -x + 5
Now we can graph these two equations on the same coordinate plane. The point where the two lines intersect represents the solution to the system of equations, which gives us the number of associates and partners assigned to the case.
When we graph these equations, we can see that the lines intersect at the point (2, 3). Therefore, the law firm assigned 2 associates and 3 partners to the case.
To check this solution, we can substitute x = 2 and y = 3 into the equations and verify that they satisfy all three equations:
400x + 1200y = 3600
400(2) + 1200(3) = 3600
x + y = 5
2 + 3 = 5
These equations are both true, so we can conclude that our solution is correct.