eqn1:= 1.x+1.y+1.z=0

eqn2:= a.x + b.y + c.z=0

eqn3:= b.c.x+c.a.y+a.b.z=1

When I try to solve this system of equations as:

solve( {eq1,eqn2,eqn3},{x,y,z} )

I get the message "Warning, solutions may have been lost"

Can you please help me to solve these equations and express my solutions in "factored form" ?