In this paper, we describe a method for computing the dimension of linear systems on a graph, which are related to linear systems of divisors on tropical curves. Tropical geometry is a discrete version of algebraic geometry, where a tropical curve can be represented by a metric graph. By reducing an algebraic curve to a graph, computing the dimension of a linear system can be thought of as a geometric problem. Specifically, we can compute the dimension of the linear system as the distance to a surface in n-dimensional space using the taxi-cab metric. Finally, we present examples of computing such dimensions of linear systems for divisors on 2-vertex and 3-vertex graphs.