var('x y z');
P1 = implicit_plot3d(x+2*y+z,(x,-6,6),(y,-6,6),(z,-6,6),colr='turquoise',alpha=0.5);
P2 = implicit_plot3d(x+z-4,(x,-6,6),(y,-6,6),(z,-6,6),color='lightcoral',alpha=0.5);
P3 = implicit_plot3d(x+y+2*z-1,(x,-6,6),(y,-6,6),(z,-6,6),color='mediumspringgreen',alpha=0.5);
(P1+P2+P3).show() #unique solution (5,-2,1)

P4 = implicit_plot3d(x+y+z-1,(x,-6,6),(y,-6,6),(z,-6,6),color='mediumspringgreen',alpha=0.5);
(P1+P2+P4).show() #no solutions

P5 = implicit_plot3d(x+y+z-2,(x,-6,6),(y,-6,6),(z,-6,6),color='mediumspringgreen',alpha=0.5);
(P1+P2+P5).show() #line of solutions