# solving simultaneous equations

Here's my code:

```
x1, y1, x2, y2 = var('x1 y1 x2 y2')
eq1 = (x1-1)*(x1-2) + (y1-3)*(y1-4) == 0
eq2 = (x2-1)*(x2-2) + (y2-3)*(y2-4) == 0
eq3 = x1+x2 == 3
eq4 = y1+y2 == 7
sols = solve([eq1,eq2,eq3,eq4],x1,y1,x2,y2,solution_dict=True)
for soln in sols:
for varbl in soln:
print "{0} : {1},".format(varbl, soln[varbl])
```

And here's my output:

```
x1 + x2 : 3,
(x1 - 1)*(x1 - 2) + (y1 - 3)*(y1 - 4) : 0,
(x2 - 1)*(x2 - 2) + (y2 - 3)*(y2 - 4) : 0,
y1 + y2 : 7,
```

I'm looking for any solutions, exact or numerical approximation. Appreciate any help. I can solve the problem by hand, but obviously that's not the point here. I'm trying to find out what I'm doing wrong and learn to use sagemath cloud properly.

Does the system have a solution? Adapting code from this answer did not seem to work.

I modified the title and retagged the post (and reformatted it) since it has nothing to do with the cloud, and the answer may be very helpful to many users.

Note: this question is a followup of this ask question.