I need help with this question parts a - d

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:
[tex]\begin{pmatrix}1&-3&0\\ 0&2&-1\\ 1&1&1\end{pmatrix}\begin{pmatrix}0\\ -3000\\ 96000\end{pmatrix}[/tex]now let's subtract row 1 from row 3
[tex]F_3-1*F_1->F_3[/tex][tex]\begin{pmatrix}1&-3&0\\ 0&2&-1\\ 0&4&1\end{pmatrix}\begin{pmatrix}0\\ -3000\\ 96000\end{pmatrix}[/tex]now let's subtract 2 times row 2 from row 3
[tex]F_3-2*F_2->F_3[/tex][tex]\begin{pmatrix}1 & -3 & 0 \\ 0 & 2 & -1 \\ 0 & 0 & 3\end{pmatrix}\begin{pmatrix}0 \\ -3000 \\ 102000\end{pmatrix}[/tex]Now we can formulate whit the third line:
[tex]3z=102000[/tex][tex]z=\frac{102000}{3}=34000[/tex]Now replace Z in F2:
[tex]2y-z=-3000[/tex][tex]2y-34000=-3000[/tex][tex]2y=31000[/tex][tex]y=\frac{31000}{2}=15500[/tex]Now replace y in F1:
[tex]x-3y=0[/tex][tex]x-3(15500)=0[/tex][tex]x=3(15500)=46500[/tex]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.