You could do like this:
syms z x1 x2 x3 x4
eqs = [-z+x1+x2; -z+x3+x4; x1+x2-x3-x4];
solve(eqs)
But it is rather pointless as there are an infinite number of solutions (three equations and five unknowns), just pick three of the values (not any three though) and you can calculate the other two.
