In[]:=
sol=Solve[{-2a1x+10/(a1x+a1y-10)+g10,-2a1y+10/(a1x+a1y-10)+g20,9/10(-2a2x(1-ix/40)+10/(a2x+a2y-10))+g30,9/10(-2a2y(1-ix/40)+10/(a2x+a2y-10))+g40,-1/2+9/10(a2x^2/40+a2y^2/40)+g50,-1/2+g60,g1*-a1x0,g2*-a1y0,g3*-a2x0,g4*-a2y0,g5*-ix0,g6*-iy0,g7*(ix-24)0,g8*(iy-24)0},{a1x,a1y,a2x,a2y,ix,iy,g1,g2,g3,g4,g5,g6,g7,g8}]
Out[]=
In[]:=
{-2a1x+10/(a1x+a1y-10)+g10,-2a1y+10/(a1x+a1y-10)+g20,9/10(-2a2x(1-ix/40)+10/(a2x+a2y-10))+g30,9/10(-2a2y(1-ix/40)+10/(a2x+a2y-10))+g40,-1/2+9/10(a2x^2/40+a2y^2/40)+g50,-1/2+g60,g1*-a1x0,g2*-a1y0,g3*-a2x0,g4*-a2y0,g5*-ix0,g6*-iy0,g7*(ix-24)0,g8*(iy-24)0}/.sol[[1]]
Out[]=
{True,True,True,True,True,True,True,True,True,True,True,True,True,True}