Algebraic Value of 2a + b

Factor both equations: $a(a + b + 1) = 14$ $b(a + b + 1) = 28$

Divide the second equation by the first: $\frac{b(a + b + 1)}{a(a + b + 1)} = \frac{28}{14} \implies \frac{b}{a} = 2 \implies b = 2a$

Substitute $b = 2a$ into the first equation: $a(a + 2a + 1) = 14$ $a(3a + 1) = 14$ $3a^2 + a - 14 = 0$ $(3a + 7)(a - 2) = 0$

Since $a$ is a natural number, $a = 2$. Then $b = 2a = 4$.

Value of $2a + b = 2(2) + 4 = 8$.