General aviation pilot reported a near miss with another aircraft when entering the traffic pattern at a non-towered airport. The pilot maneuvered to avoid a collision with the other aircraft who was not communicating their position.

Narrative

We (aircraft X) were on a 45 Entry for Runway 17 about 3-5 nm inbound BXK for right downwind; at 2000 feet traffic pattern altitude. This is when noticed aircraft Y was on our 3´o clock at 2000 feet heading directly into our flight path with a possible midair collision. No call was made by them on CTAF BXK. After having them inside we tried calling them on the CTAF as well as on the Air to Air frequency (128.92) and got no response. They did not take any evasive action leading us to initiate a descent to avoid a collision. Thus leading us to be below traffic pattern altitude (less than 1000 ft AGL). Climbing was no good available option due to the risk of the other traffic climbing as well. Right turn would have led us straight into them; neither would have been a left turn an option due to flying parallel to the traffic. Progress check instructor was on board of aircraft Y but did intervene.According to procedures they should have been at 3000 ft at Arlington town. Above Arlington town they should have started a turn towards the north. But they turned early and crossed the traffic pattern and the 45 Entry for the downwind at BXK at traffic pattern altitude without any intention to join the pattern.Suggestions: Comply to company procedures. Monitor and transmit on frequency. Do not fly at traffic pattern altitude close the BXK when crossing this close. More Emphasis on scanning for traffic and situational awareness.