Can scheme be covered by affine schemes like varieties?

Question

A scheme, by definition, is a locally ringed space in which every point has an open neighborhood $U$ such that the topology space $U$, together with the restricted sheaf, is an affine scheme(isomorphic to the spectrum of some ring). And as we know, a variety can by covered by affine open subsets so that we can deal with problems locally. Thus, I wonder whether a scheme can be covered by affine schemes and using the local property of spectrum to solve problems?

Answer 1

Yes:

A scheme is a locally ringed space $X$ admitting a covering by open sets $U_i$, such that each $U_i$ (as a locally ringed space) is an affine scheme. In particular, $X$ comes with a sheaf $O_X$, which assigns to every open subset $U$ a commutative ring $O_X(U)$ called the ring of regular functions on $U$. One can think of a scheme as being covered by "coordinate charts" which are affine schemes. The definition means exactly that schemes are obtained by gluing together affine schemes using the Zariski topology.

from wikipedia: scheme#definition

Answer 2

Yes, it is already in the definition you give. If $(X,\mathcal{O}_X)$ is a scheme, then by definition every point $x\in X$ has an open neighbourhood $U_x$ such that $(U_x,\mathcal{O}_X\vert_{U_x})$ is an affine scheme. Then $\{U_x\}_{x\in X}$ is an affine open cover of $X$.