en•gaged ( n-g jd )
adj.
1. Employed, occupied, or busy.
2. Committed, as to a cause.
3. Pledged to marry; betrothed: an engaged couple.
4. Involved in conflict or battle.
5. Being in gear; meshed.
6. Partly embedded in, built into, or attached to another part, as columns on a wall.
The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company. Updated in 2003. Published by Houghton Mifflin Company. All rights reserved.

ThesaurusLegend: Synonyms Related Words Antonyms
Adj.    1.    engaged - having ones attention or mind or energy engaged; "she keeps herself fully occupied with volunteer activities"; "deeply engaged in conversation"
occupied
busy - actively or fully engaged or occupied; "busy with her work"; "a busy man"; "too busy to eat lunch"; "the line is busy"
2.    engaged - involved in military hostilities; "the desperately engaged ships continued the fight"
involved - connected by participation or association or use; "we accomplished nothing, simply because of the large number of people involved"; "the problems involved"; "the involved muscles"; "I don't want to get involved"; "everyone involved in the bribery case has been identified"
    3.    engaged - reserved in advance
booked, set-aside
reserved - set aside for the use of a particular person or party
4.    engaged - (of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line); "her line is busy"; "receptionists' telephones are always engaged"; "the lavatory is in use"; "kept getting a busy signal"
in use, busy
occupied - held or filled or in use; "she keeps her time well occupied"; "the wc is occupied"
5.    engaged - (used of toothed parts or gears) interlocked and interacting; "the gears are engaged"; "meshed gears"; "intermeshed twin rotors"
intermeshed, meshed
geared - equipped with or connected by gears or having gears engaged
6.    engaged - having services contracted for; "the carpenter engaged (or employed) for the job is sick"
employed - having your services engaged for; or having a job especially one that pays wages or a salary; "most of our graduates are employed"
7.    engaged - built against or attached to a wall; "engaged columns"
architecture - the discipline dealing with the principles of design and construction and ornamentation of fine buildings; "architecture and eloquence are mixed arts whose end is sometimes beauty and sometimes use"
connected - joined or linked together
8.    engaged - pledged to be married; "the engaged couple"
affianced, betrothed, pledged, bespoken
committed, attached - associated in an exclusive sexual relationship

谢谢指正，已经改了过来了。

见
http://www.thefreedictionary.com/
因此是不能用engaged 的
另外纸写reserved即可

“Reserved” is widely used in many conferences. Since your conference is to be held in China, please consider to use bilingual sign “留座 Reserved”

今天我查了字典，知道engaged是错的。
昨天突然想到是因为一次中学时代的英语课上，老师讲过电话占线可以用engaged。
今天知道它只能用在时间的预订上。

茅茅，你家的英语老师绝对是个文人也，电话占线最简单的字是：The line is busy or Somebody is on the line.

应该都可以吧

Booked也可以当成预留的、预定的吧。如预定机票、饭店订个房间或座位等。book your plane ticket. Book a room in the hotel。 This table is booked or reserved.

booked有当事人主动的意思
而reserved则没有这个意思吧

红狐小妹，两个都可以是主动和被动吧。