What Happens to dirty pages if the system fails before the next checkpoint?
Both the log and data page entries are made in RAM and committed to
  disk later by a Checkpoint.


This statement is not completely true. It is correct that data pages are written to disk by Checkpoint (and Lazy Writer). Log records, however, are physically written to disk when the transaction is committed to guarantee transaction durability. A committed transaction data will never be only memory resident (barring delayed durability).

All data modifications are first written to the log (write-ahead logging) and dirty pages written afterward. Pages and log records may include both committed and uncommitted data on disk. 

Regardless of the recovery model, SQL Server scans the log during crash recovery to the last checkpoint, rolls forward all data modifications from that point forward, and finally rolls back uncommitted transactions.