# A bug with solve xy=x ?

For solving the equation "xy=x", we can do:

```
sage: x,y=var('x,y')
sage: solve([x*y==x],[x,y])
[x == 0]
```

But this is not the complete solution.

We need to add the trivial equation "0==0" for having the complete solution:

```
sage: solve([x*y==x,0==0],[x,y])
[[x == 0, y == r1], [x == r2, y == 1]]
```

Is it a bug ?

Is it a bug? A good question. If we change the order of x,y to solve([x*y==x],[y,x]) , we get y==1 as solution. Obviously only the first variable is used as far as there is only one equation. IMHO that's not a bug, but it would be nice, if Sage could add the trivial equation automatically.