How to prove that $V=\left\{\left(2x-1,x\right)\vert x \in \mathbb{R}\right\}$ is not a vector space? How to prove that $$V=\left\{\left(2x-1,x\right)\vert x \in \mathbb{R}\right\}$$ is not a vector space?

Is there an $x \in \mathbb{R}$ that would make $(2x -1, x ) = (0,0)$? well, we would have 
$$ x = \frac{1}{2} \; \; \text{and} \; \; x = 0 $$
which is impossible
