Condition for Planes to be Parallel

Let $$P = \alpha_1 x_1 + \alpha_2 x_2 + \alpha_3 x_3 = \gamma$$ be a plane in $$\mathbb{R}^3$$.

Then the plane $$P'$$ is parallel to $$P$$ iff $$P'$$ is the set of all $$\left({x_1, x_2, x_3}\right) \in \mathbb{R}^3$$ where $$\exists \gamma' \in \mathbb{R}: \alpha_1 x_1 + \alpha_2 x_2 + \alpha_3 x_3 = \gamma'$$.