Can a PCI-X card be plugged into a PCI slot not the other way around as I have only a PCI card slot?

Can it? Sometimes, in PCI 3.3V slots(PCI rev. 2.2 or newer).

But should it? No, a PCI-X card should be not be inserted into PCI slot.

Putting a faster card(e.g., PCI-X, 64-bit/133MHz) into a slower slot(PCI 2.2, 32-bit/33MHz) will force the card to transfer data much slower than what it is capable of doing.

IOW, even if PCI-X cards sometimes work in PCI Revision 2.2 or newer slots it is pointless to do that since it defeats the purpose of having a PCI-X card, namely wider bandwidth. PCI-X(133MHz) cards are capable of approx 1.0GB/s transfers while PCI (32-bit/33MHz) can only handle approximately 0.1GB/s, theoretically. In reality both do somewhat less ... but putting a 1.0GB/s card into a 0.1GB/s slot is wasting perfectly good bandwidth(and the money spent to get it!).

If you only have PCI(32-bit) slots, then buy only PCI(32-bit) cards.

All PCI cards that adhere to PCI revision 2.2 or newer specifications can be used in PCI-X slots. ( Note that most cards are now manufactured to meet PCI 2.2 or 2.3 specifications. )

However the transfer rate/speed will not necessarily increase because the card is in a slot capable of faster transfers.

PCI slots that are older, prior to PCI rev. 2.2, should physically block the insertion of a normal PCI-X card into the slot.

PCI cards that are older, prior to PCI rev. 2.2, should be physically blocked from being inserted into PCI-X slots.

Both of the latter of course depend upon the manufacturer of the expansion card following the PCI specifications. Unfortunately not all manufacturers do that(so be careful!).

As always there are various additions and exceptions but confusion is the general rule when they are considered so let's leave it as:

Long card in short slot: no, it wastes bandwidth and money.

Short card in long slot: ok, if it inserts without undo insertion force(but it also wates available bandwidth).