Certainly ^^
But what "Bernie" was doing was the result of thinking that a second equation was distinct from the first, then combining the two to get that they are both the same.
Eg y+1=x=>y=x-1, and 2y+2=2x, replacing x-1 for y becomes 2x-2+2=2x=>x=x. The equations were simply the same relation from the start, so nothing new would come from using one on the other.
On the other hand, if the equations were different, and you had as many of those as unknowns, you would solve the system. Eg y=x-1 and x^2-y^2=9=>x^2-x^2+2x-1=9=>2x=10=>x=5=>y=4.