linear algebra - Two vectors are linearly independent?

Let $x, y, z$ be vectors in vector space $V$. Suppose $z \notin L(x,y)$
, where $L(x,y)$ is the linear span of $x, y$.

Show that $x, y$ are linearly independent iff x+z, y+z are linearly independent.

I can easily show that $x, y$ are linearly independent implies linear independence of $x+z, y+z$. But I have a trouble with showing converse!. I want someone who help me~~