Suppose the solutions of a homogeneous system of five linear equations in six unknowns are all multiples of one nonzero solution. Will the system necessarily have a solution for every possible choice of constants on the right sides of the equations? Explain.

Consider the provided question,
Given a system of five linear equations in six unknowns are all multiples of one nonzero solution.
It can be written as,
$Ax=0$ where $A=5\times 6$ matrix
$dim(NulA)=1$ because all solutions of $Ax=0$ are multiples of nonzero solution
We have to explain that the system necessarily have a solution for every possible choice of constants on the right sides of the equations.
Since,A is $5\times 6$ matrix $n=6$
$rank(A)=n-dim(NulA)=6-1=5$
Image of A is 5 dimensional subspace of $R^5$ (because A has 5 rows)
So,$Col(A)=$$R^5$
This means that Ax=b has a solution for every b