解：?$(1)$?∵?$x-y=3$?
∴?$x=y+3$?
∵?$x＞2$?
∴?$y+3＞2$?
∴?$y＞-1$?
∵?$y＜1$?
∴?$-1＜y＜1，$?①
同理得：?$2＜x＜4，$?②
由?$①+②$?得?$-1+2＜y+x＜1+4$?
∴?$x+y$?的取值范圍是?$1＜x+y＜5$?
?$(2)$?∵?$x-y=a$?
∴?$x=y+a$?
∵?$x＜-1$?
∴?$y+a＜-1$?
∴?$y＜-a-1$?
∵?$y＞1$?
∴?$1＜y＜-a-1，$?①
同理得：?$a+1＜x＜-1，$?②
由?$①+②$?得?$1+a+1＜y+x＜-a-1+(-1)$?
∴?$x+y$?的取值范圍是?$a+2＜x+y＜-a-2$?
