If a + b + c = 12, a + b = 4, and a + c = 7, what is the value of a?

Question: If a + b + c = 12, a + b = 4, and a + c =7, what is the value of a?
Solution:
Given that,
a + b + c = 12 .......(1)
a + b = 4 ......(2)
And a + c = 7 .......(3)

Now, Adding (2) and (3)
a + b + a + c = 4 + 7 = 11
⇒ 2a + b + c = 11 .......(4)

So, (4) - (1) ⇒
⇒ (2a + b + c) - (a + b + c) = 11 - 12
⇒ 2a + b + c - a - b - c = - 1
∴ a = - 1