Solve the system x1 + x2 = -5 x2 + x3 = 2 x3 + x4 = 5 x1 + x4 = -2?

x1 + x2 = -5
x2 + x3 = 2
x3 + x4 = 5
x1 + x4 = -2
No solution.

The determinant of
1 1 0 0
0 1 1 0
0 0 1 1
1 0 0 1
= 0 so there is not a unique solution.

Here's a solution:
-2
-3
5
0

Here's another:
-7
2
0
5

I don't understand the what the additional information is trying to say.

Solve the system
x1 + x2 = -5
x2 + x3 = 2
x3 + x4 = 5
x1 + x4 = -2

Additional information on the problem:
[x1 x2 x3 x4] = ______________+ s_______________ where s is a free variable.