Vectors are mathematical representations of distance and direction information that take the form of line segments where length represents distance and orientation in space represents direction. Vector-based models have proven beneficial in understanding the spatial behavior of a variety of species in tasks that require landmark-based navigation via vector addition and vector averaging to determine a location. Extant research regarding vector-based representational and computational accounts of landmark-based navigation has involved tasks that required solving for one unknown (i.e., a location). Using a novel landmark-based navigation task, we provide evidence consistent with a form of vector algebra that involves solving two simultaneous equations with two unknowns in order to determine a location in space. Results extend vector-based accounts of landmark-based navigation and provide a novel methodological approach to the testing of mobile organisms.