Nice set of equations?

$(ax^b)'=cx^d$ , where $a\neq b\neq c\neq d$ and a,b,c,d are integers where $0 \leq a,b,c,d\leq 9$

There should be 3 sets of values of a, b, c and d. Let the first set be ${a_1, b_1, c_1, d_1}$ , the second set be ${a_2, b_2, c_2, d_2}$ and the last set be ${a_3, b_3, c_3, d_3}$ .

Substitute the values into the equations $a_nx+b_ny+c_nz=d_n$ where n=1, 2, 3.

Solve for x, y and z.

x+y+z=?