# How to find the reduced echelon form of a homogenous linear system given only the solutions?

I'm having a hard time understanding this question:

Determine the reduced echelon form of the homogeneous linear system of three equations in variables $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ such that $x_{1}, x_{2}, x_{4}$ are leading variables; $x_{3}, x_{5}$ are free variables and which has solutions

$$\begin{pmatrix}2 \\-1\\1\\0\\0 \end{pmatrix} \quad\text{and}\quad \begin{pmatrix}-3 \\2\\0\\-4\\1 \end{pmatrix}$$