First Officer reported the loss of both B Hydraulic System Pumps led to the loss of the B Hydraulic System. The flight crew continued to destination airport and made a safe landing.

Narrative

First day and first leg of trip. I was pilot flying (PF). As we were approaching our cruise altitude of FL 370 a caution light illuminated which had the Captain and I staring up at the ENG 2 LOW PRESSURE light. The Captain ran the QRH which just directed HYD PUMP switch (affected side) OFF. The B System Pressure remained in the normal range and the hydraulic quantity held at 106%; so we decided to continue to the original destination. Dispatch was notified through ACARS of the situation. 90 minutes later; story time was interrupted by the illumination of ELEC 1 LOW PRESSURE light and I noticed the Hydraulic B quantity dropped rapidly to 0%. The Captain then ran the LOSS OF SYSTEM B QRH. A discussion was had regarding if the situation required a diversion to a longer runway. After being notified; Dispatch ran Stopping Performance numbers; which still resulted in positive numbers; and a now required 30 minutes of brake cool down off the gate. A request for priority handling was made at this point. Twenty minutes after loss of System B; the ENG 1 LOW PRESSURE light illuminated (now the A side is acting up). QRH directed the affected switch be turned off. Realizing that communication via ACARS was hindering our ability to share a mental model with Dispatch and the collection of required data; in a timely manner; I requested a nearby Ops Station to patch our flight through to Dispatch. The Captain conversed with ZZZ while I handled COMM 1. The remaining ELEC 2 pump was providing adequate reduced flow pressure and the A Hydraulic System retained its quantity.Dispatch ran Runway performance numbers for Loss of System A and B; just in case; which still yielded positive stopping performance. After considering the advantages of using the HUD for the approach; the Captain and I switched flying roles (I was now pilot monitoring). We ran the deferred items for the LOSS OF SYSTEM B and received vectors for a long final approach for a flaps 15 landing. A good landing was made; and after the Captain exited the runway; we taxied to a spot to wait out our brake cool down; all the while being monitored by the local Airport Rescue and Firefighting (ARFF) who were surrounding the aircraft. While allowing the brakes to cool; several of our Company aircraft reported that fluid was leaking from the underside of Engine 2 (The ARFF Crew was concerned that it may be fuel.). The Captain then directed me to shut Engine 2 off. In the non-normal state that we then found ourselves; we elected to get towed into the gate.