I need a help with prooving that a given set is a convex set:
$\{ x \in R^n | Ax \leq b, Cx = d \}$
I know the definition of convexity: $X \in R^n$ is a convex set if $\forall \alpha \in R, 0 \leq\alpha \leq 1$ and $\forall x,y \in X$ holds: $\alpha x + (1 - \alpha)y \in X$.
I tried to apply this for my set but I dont know how to prove that it works... Thanks in advance for any tips.