Equivalence of systems of equations with solution zero.

I understood that two systems of linear equations are equivalent if one can be obtained by the linear combination of the other system and vice versa. But can those two systems of equations be equivalent even if the solution $x_i=0? (1\le i\le n)$.Example set :

$x_1-x_2=0 ;$

$2x_1+x_2=0$

and

$3x_1+x_2=0 ;$

$x_1+x_2=0$

I got only zero as solution for both $x_1$ and $x_2$. Are these systems of equations equivalent?

• what does equivalence mean here? – piepi Jun 12 '16 at 16:50
• @piepi Look carefully: it's written in the first line. If and only if the equations of one are linear combinations of the equations of the other one and viceversa. – user228113 Jun 12 '16 at 16:51
• math.stackexchange.com/questions/46050/… – piepi Jun 12 '16 at 17:11