Answer
$(1, -1, 1)$
Work Step by Step
Step 1. Subtract equation 2 from equation 1 and get $ax-bx=a-b$ thus $x=1$ (given $a\ne b$)
Step 2. Subtract equation 3 from equation 2 and get $bx-cx+by-cy=0$ or $(b-c)(x+y)=0$. Since $b\ne c$ we have $y=-x=-1$
Step 3. Plug-in the numbers from above to equation 3 to get $z=1-x-y=1$ (given $c\ne 0$)
Step 4. Conclusion: $(1, -1, 1)$
