In many geomatics, computer vision, and computer-aided applications, coordinate transformations are needed to transform from one coordinate system to another, especially in geodesy and photogrammetry. In photogrammetry one of the important coordinates transformation methods used to transform photo coordinates is the 2D affine transformation which takes into consideration the change in the differences in scale factor in the x and y directions. In this paper, a new method for computing the 2D affine transform parameters will be introduced, the problem of the 2D affine transform method has been solved by Gaussian elimination with pivoting. We have derived equations by which to find transformation parameters. Geometric transformation is a technique used to define the properties of common features between different images using the same coordinates basis, This method can be effectively used in image processing and computer vision to facilitate the computation process throughout eliminating the need for solving the inverse of the matrix.