A.
You have to assign the variables to the universities, I will do it like this:
x=Austin
y=Miami
z=California
B.
Now interpret the statement and write the equations:
Austin has 3 times the students that Miami has.:
x=3y
Berkley has 3000 students more than Miami twice:
z=3000+2y
The sum of all is 96000
x+y+z=96000
Now let all the variables on the left side of the equations and the constants on the right side. So the equations system looks like this:
x-3y = 0
2y-z = -3000
x+y+z = 96000
C.
Set the matrix:

now let's subtract row 1 from row 3


now let's subtract 2 times row 2 from row 3


Now we can formulate whit the third line:


Now replace Z in F2:




Now replace y in F1:



So we have:
x=46500 students
y=15500 students
z=34000 students
D.
We can interpret that:
The University of Texas has 46500 students, The University of Miami has 15500 and the University of California has 34000 students.