Consider a large linear system where $A}_{n$ is a $n\times n$ matrix with independent real standard Gaussian entries, $1}_{n$ is a $n\times 1$ vector of ones and with unknown the vector $x}_{n$ satisfying $x}_{n}={1}_{n}+\frac{1}{{\alpha}_{n}\sqrt{n}}{A}_{n}\phantom{\rule{0}{0ex}}{x}_{n$ We investigate the (componentwise) positivity of the solution $x}_{n$ depending on the scaling factor $\alpha}_{n$ as the dimension $n$ goes to $\infty$. Such linear systems arise as solutions at equilibrium of large Lotka-Volterra systems of differential equations, widely used to describe large biological communities with interactions such as foodwebs for instance. In the domaine of positivity of the solution $x}_{n$, we establish that the Lotka-Volterra system of differential equations whose solution at equilibrium is precisely $x}_{n$ is stable in the sense that its jacobian $\mathcal{J}({x}_{n})=\text{diag}({x}_{n})\left(-{I}_{n}+\frac{1}{{\alpha}_{n}\sqrt{n}}{A}_{n}\phantom{\rule{0}{0ex}}{x}_{n}\right)$