PAY with CASH, CHECK/CHEQUE/CREDIT CARD
pay [form of money]
pay in [form of money]
pay with [form of money]
pay by [method of payment]
pay with a [method of payment]
* forms of money: cash, hard currency, dollars, ready money, silver, etc.
* methods of payment: check/cheque, credit card, etc.
For example:
pay cash
pay hard currency
pay dollars
pay ready money
pay silver
pay in cash
pay in hard currency
pay in dollars
pay in ready money
pay in silver
pay with cash
pay with hard currency
pay with dollars
pay with ready money
pay with silver
pay by check/cheque but not pay check/cheque
pay by credit card but not pay credit card
pay with a check/cheque but not pay with check
pay with a credit card but not pay with credit
Conclusion:
We can say pay cash, pay in cash or pay with cash.
We can say pay by cheque/credit card, but not pay check/cheque/credit card.
We can say pay with a check/cheque/credit card but not pay with cheque/credid card.
Note:
"pay by cash" is also used, but less commonly because some people suppose that "by" is used for "methods of payment: check, credit card, ect." (showing how or in what way the payment is done).