70.3k views
1 vote
If ( a + b - c = 7 ) and ( ab = bc + ac ), find ( a + b + c ).

a. 3
b. 7
c. 10
d. 14

User Ryber
by
7.7k points

1 Answer

6 votes

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.

User CC Inc
by
8.5k points