How to figure out which of three equations: $y=-2x+1, y=2x+1, y=x+1$ is linearly dependent on the others? I have three equations: 
$$y=-2x+1$$
$$y=2x+1$$
$$y=x+1$$
I am trying to see which of these is linearly dependent on the others. Normally I can just eyeball it, but here it is very hard to see. Does anyone know a general method to see which equation is causing the linear dependency? thanks!
 A: In truth, a set of equations itself is linearly (in)dependent; not some equation is linearly dependent on another one, although this is a common linguistic abuse.
As others have said, any two equations from your set of three form a linearly independent (sub)set, but the three of them form a linearly dependent set. There's no particular one that depends on the others.
A: The problem is that the system of equations is inconsistent in this case. Solving the first two equations, we get y = 1, x = 0, but that is obviously not what the last equation wants.
There is no way you can construct the linear dependency in this case.
A: Add $3/4$ times the second to $1/4$ times the first and you get the third. So in that sense, the third depends on the first two.
But add $-3$ times the second to $4$ times the third and you get the first. So in that sense, the first depends on the latter two.
Similarly, there is a way to express the middle one as "depending" on the first and last.
So it's not about "which one" depends on the other two. As a whole, the set is a "dependent" set. 
