The entered GCPs are rarely perfectly located and are even more rarely perfectly representative of the distortion in the rest of the image, but the algebraic solution, which appears to be a perfect match, masks any error. To avoid this, it is common to create many more than the minimal required set (creating an overdetermined system), and use least squares regression to derive a set of function parameters that most closely matches the points.
GCPs inserted are typically not precisely located and rarely accurately represent the distortion in the rest of the image. The algebraic solution appears to be an exact match but hides any errors. To avoid this, it is common practice to create a larger set than necessary (forming an overdetermined system) and use least squares regression to derive function parameters that closely fit the points.