This study presents a cost-effective and environmentally friendly approach for the simultaneous determination of a veterinary binary mixture comprising doxycycline hydrochloride (DOX) and tylosin tartrate (TYZ) utilizing UV spectroscopy alongside dimension reduction algorithms (DRAs). Seventeen DRAs were evaluated, and their performances were compared based on four metrics: mean squared error (MSE), mean absolute error (MAE), median absolute error (MedAE), and coefficient of determination (R2). Based on the performance indices, Isomap algorithm demonstrated the highest predictive capacity among all DRAs. MSE, MAE, MedAE and R2 values of (0.38, 0.28, 0.19 and 0.999) and (0.08, 0.26, 0.22 and 0.998) were obtained for calibration and test datasets, respectively across a concentration range 4.67–30 μg mL−1 for DOX. MSE, MAE, MedAE and R2 values of (0.54, 0.34, 0.19 and 0.994) and (0.07, 0.19, 0.07 and 0.998) were obtained for calibration and test datasets, respectively across a concentration range 3.51–24 μg mL−1 for TYZ. The developed method underwent validation utilizing the accuracy profile approach. An ecological impact assessment was carried out employing six greenness evaluation tools: The Green Solvent Selection Tool (GSST), National Environmental Methods Index (NEMI), the Assessment of Green Profile (AGP), carbon footprint analysis, Analytical Greenness Calculator (AGREE), and Complementary Green Analytical Procedure Index (Complex GAPI). Additionally, we applied blueness and whiteness assessments using Blue Applicability Grade Index (BAGI) and Red-Green-Blue 12 (RGB 12) algorithms, respectively. The proposed method demonstrated higher GSST scores, a more "green" profile in NEMI, a superior AGP profile, and better environmental sustainability in Complex GAPI. The calculated carbon footprint value was 0.0002 kg CO2 equivalent per sample, The AGREE score was 0.87, BAGI was assessed at 72.5, and the whiteness assessment by the RGB12 algorithm was 89.6. Statistical comparison of the proposed method with a previously reported HPLC method for dosage form analysis revealed no significant differences at a 95% confidence level. This study highlights the novelty of combining UV spectroscopy with dimension reduction algorithms, offering significant advancements over traditional UV and chemometric methods for the analysis of these drugs. This approach not only enhances the efficiency and accuracy of determining active ingredients in pharmaceutical dosage forms but also contributes to environmental sustainability.