Solving Matix in lorg # of var [around 400]

How about if I just want to solve any size of matrix in C++, is there any code I could just use.
Since an small part of my program needs to solve lots of equations like :

b+f+d = 3
a+b+f+i+h =2
and so on
very fast

and the number of variables could be more than 400 !!! so memory uses and speed is very VERY VERY important !!!! I do not care about the memory, but the SPEED is important ;) [sorry I am keep saying that]

is there any solution out there I could use any lib or code???
Thanks