Equivalence of Linear Equation Systems: Mutual Implications of Linear Combinations

Question

Imagine we have two sets of linear equations called System $\rm{I}$ and System $\rm{II}$. If the equations in $\rm{I}$ can be written as combinations of those in $\rm{II}$, can we also say that the equations in $\rm{II}$ can be written as combinations of those in $\rm{I}$? If that's the case, we can conclude that these systems are equivalent.