eqns := { z = 4 * x1 + 5 * x2 ,
         x3 = 8 - x1 - 2 * x2 ,
         x4 = 5 - x1 -  x2 ,
         x5 = 8 - 2 * x1 -  x2 } ;

solve( eqns, {z,x1,x2,x5} ) ;

dual_eqns := { w = -8*y1-5*y2-8*y3 ,
  y4 = -4+y1+y2+2*y3 ,
  y5 = -5+2*y1+y2+y3 } ;

solve( dual_eqns , {y2,y1,w} ) ;