If (2a - 2b) = 2 and (3a + 2b) = 8 then find the value of (3a + 4).

Question: If (2a - 2b) = 2 and (3a + 2b) = 8 then find the value of (3a + 4).

Solution:
2a - 2b = 2 ...........(1)
3a + 2b = 8 .............(2)

From (1) we get,
2a - 2b = 2
⇒ a - b = 1
⇒ a = b + 1 .......(3)

From (2) we get,
3(b + 1) + 2b = 8
⇒ 3b + 3 + 2b = 8
⇒ 5b = 5
∴ b = 1
From (3) we get,
a = 1 + 1
∴ a = 2

Now,
3a + 4
= (3 × 2) + 4
= 6 + 4
= 10