[Math] Write down a homogeneous linear system of three distinct equations in three variables that has the non-trivial solution $(x, y,z) = (1,2, 4)$

Question

Write down a homogeneous linear system of three distinct equations in three variables
that has the non-trivial solution $(x, y, z) = (1,2, 4)$.

I am confused on how to approach this problem

Answer 1

$$y=2x;\quad z=2y;\quad z=4x.$$