Question: How to solve system of equation simultaneously ?

sys := {x^3*a[1]*b[0]+x*a[1]^3*b[0]-x^3*a[0]-x*a[0]*a[1]^2+omega*a[1]*b[0]-omega*a[0] = 0, -x^3*a[-1]*b[-1]^2*b[0]+x^3*a[0]*b[-1]^3-omega*a[-1]*b[-1]^2*b[0]+omega*a[0]*b[-1]^3-x*a[-1]^3*b[0]+x*a[-1]^2*a[0]*b[-1] = 0, -4*x^3*a[1]*b[0]^2+4*x^3*a[0]*b[0]+8*x^3*a[1]*b[-1]+2*x*a[0]*a[1]^2*b[0]+2*x*a[1]^3*b[-1]+2*omega*a[1]*b[0]^2-8*x^3*a[-1]-2*x*a[-1]*a[1]^2-2*x*a[0]^2*a[1]-2*omega*a[0]*b[0]+2*omega*a[1]*b[-1]-2*omega*a[-1] = 0, 4*x^3*a[1]*b[-1]*b[0]^2-4*x^3*a[-1]*b[0]^2-32*x^3*a[1]*b[-1]^2+4*omega*a[1]*b[-1]*b[0]^2-32*x^3*a[-1]*b[-1]+4*x*a[-1]*a[1]^2*b[-1]+4*x*a[0]^2*a[1]*b[-1]-4*omega*a[-1]*b[0]^2+4*omega*a[1]*b[-1]^2-4*x*a[-1]^2*a[1]-4*x*a[-1]*a[0]^2-4*omega*a[-1]*b[-1] = 0, 4*x^3*a[-1]*b[-1]*b[0]^2-4*x^3*a[0]*b[-1]^2*b[0]+8*x^3*a[1]*b[-1]^3-8*x^3*a[-1]*b[-1]^2-2*omega*a[-1]*b[-1]*b[0]^2+2*omega*a[0]*b[-1]^2*b[0]+2*omega*a[1]*b[-1]^3-2*x*a[-1]^2*a[0]*b[0]+2*x*a[-1]^2*a[1]*b[-1]+2*x*a[-1]*a[0]^2*b[-1]-2*omega*a[-1]*b[-1]^2-2*x*a[-1]^3 = 0, x^3*a[1]*b[0]^3-x^3*a[0]*b[0]^2-18*x^3*a[1]*b[-1]*b[0]+omega*a[1]*b[0]^3-5*x^3*a[-1]*b[0]+23*x^3*a[0]*b[-1]+x*a[-1]*a[1]^2*b[0]+x*a[0]^2*a[1]*b[0]+5*x*a[0]*a[1]^2*b[-1]-omega*a[0]*b[0]^2+6*omega*a[1]*b[-1]*b[0]-6*x*a[-1]*a[0]*a[1]-x*a[0]^3+5*omega*a[-1]*b[0]-omega*a[0]*b[-1] = 0, -x^3*a[-1]*b[0]^3+x^3*a[0]*b[-1]*b[0]^2+5*x^3*a[1]*b[-1]^2*b[0]+18*x^3*a[-1]*b[-1]*b[0]-23*x^3*a[0]*b[-1]^2-omega*a[-1]*b[0]^3+omega*a[0]*b[-1]*b[0]^2+5*omega*a[1]*b[-1]^2*b[0]-x*a[-1]^2*a[1]*b[0]-x*a[-1]*a[0]^2*b[0]+6*x*a[-1]*a[0]*a[1]*b[-1]+x*a[0]^3*b[-1]-6*omega*a[-1]*b[-1]*b[0]+omega*a[0]*b[-1]^2-5*x*a[-1]^2*a[0] = 0}