We can rewrite the problem as:
x + y = 8
z - x = 6
----------
13 8
This gives us 3 unique linear equations:
x + y = 8 (and also y + x = 8 vertically but that's the same thing)
z - x = 6
x + z = 13
Rewriting the second equation as -x + z = 6 we can solve for z by adding the two equations:
x + z = 13
-x + z = 6
---------
2z = 19
Thus z = 9.5. Substituting for z in the equations above gives us x = 3.5 which then gives us y = 4.5, therefore:
3.5 + 4.5 = 8
9.5 - 3.5 = 6
-----------
13 8
