Tile-securing system and related methods

A tile-securing system comprising:

• a polymeric wedge component positioned between two adjacent tiles that are in plane and the polymeric wedge component contacting a side edge of each adjacent tile, wherein the polymeric wedge component exerts a force against both side edges, the polymeric wedge component comprising of a longitudinal axis, wherein a width of the polymeric wedge component tapers from one end of the longitudinal axis to an opposite end of the longitudinal axis;
• a fastener exerting a downforce on the polymeric wedge component, wherein the force being exerted against both side edges increases as the downforce increases, and wherein portions of the polymeric wedge component compress and flatten due to pressure as the downforce increases and as the force being exerted against both side edges increases;
• the polymeric wedge component being secured to a solid substrate by a portion of the fastener being fixedly positioned within the substrate;
• and
• the polymeric wedge component and fastener positioned between the two adjacent tiles at a side-edge portion of each tile that is approximately at a midpoint of each adjacent tile's side-edge portion.