Linear equations

let no. of pigeons be $x,$ then no. of rabbits are $300-x.$

no. of legs one pigeons $= 2,$

no. of legs in total pigeons $= 2x,$

no. of legs one rabbit $=4.$

no. of legs in total rabbits $= 4 (300-x) = 1200-4x,$ so $\begin{aligned} 2x+1200-4x &=750 \\ -2x+1200 &=750 \\ -2x & =750-1200 \\ -2x &= -450 \\ \implies x &=\frac{-450}{-2} = 225. \end{aligned}$ Therefore, no. of pigeons is 225.

A pigeon has two legs and a rabbit has four legs and of course a pigeon has one head and a rabbit has one head. Letting $p$ and $r$ represent the number of pigeons and rabbits, respectively, yields into two equations.

$p+r=300$ $\color{#D61F06}(1)$

$2p+4r=750$ $\color{#D61F06}(2)$

Solving the system of equations by any method, we get $p=225$ and $r=75$ .

The desired answer is $\large{\color{#3D99F6}\boxed{225}}$ .