The task is to solve the fourth equation:
a + b =7
a + c = 11
b + c = 10
a + b + c = ?
The common attempt to solve this problem is to calculate the values of each variable by combining all of the equations, like so:
a = 7 − b
a = 7 − (10 − c)
a = 7 − (10 − (11 − a))
a = 4.
After calculating each of the variable values, the fourth equation is simple to solve. This representation focuses around idea of variables as unknown values that need to be solved and can be commonly found being thought in primary and secondary schools. It requires a lot of computations, but it gives us all of the primary values of this problem (though this data can be useful, it is not necessary for this problem).
When attempting to relieve themselves of the burden to compute all variable values, some solvers combine equations together in order to reach the fourth
equation form, like so:
(a + b) + (a + c) + (b + c) = 7 + 11 + 10
a + b + c = ((a + b) + (a + c) + (b + c))/2 = (7 + 11 + 10)/2 = 14
This approach is strongly preferred according to computational complexity, as it requires the minimum number of mathematical functions to be solved; two additions and a division. To view the problem through this perspective can be extremely beneficial, but it is very rarely observed.