Final answer:
The sum a + b + c equals 7, as the given conditions imply that a and c are equal in magnitude but opposite in sign, canceling each other out and leaving b alone which equals 7.
Step-by-step explanation:
To solve the question (a + b - c = 7) and (ab = bc + ac), we need to find the value of (a + b + c). However, the second equation, ab = bc + ac, can be rewritten as a(b-c) = c(b-a). If neither a, b, nor c is zero, we can divide both sides by (b-c) and (b-a), which gives us a = c. Then, we already know from the first equation that a + b - c = 7. If a = c, we can then substitute c with a, which gives us a + b - a = 7, simplifying to b = 7.
Substituting back into the first equation, we get a + 7 - a = 7, which means any value of a will satisfy these conditions as long as a = c. Thus any number plus its own negative will result in zero. Hence, the sum a + b + c equals to b = 7, since a + c = 0.