I have never liked span questions, so I could use some help with this.

First, suppose that $\displaystyle V$ is a vector space over a field $\displaystyle F$.

Now suppose $\displaystyle x,y,z\in V$ satisfies $\displaystyle x+y+z=0$. Prove that $\displaystyle span\{x,y\}=span\{y,z\}$.