We note that in the first equation, corresponding to the first mesh, the coefficient of the first current is the sum of the resistances associated with the first mesh, and the coefficient of the other mesh current is the negative of the negative of the resistance common to that mesh and the first mesh. The right side of the first equation is the net voltage rise in the direction of traversal due to voltage sources in the first mesh. The same pattern applies to each equation. On the left side of the mesh k equation, the coefficient of the other mesh currents are the negatives of the resistances on the boundary between their meshes and mesh k. The right side of the mesh k equation consists of the net voltage rise in this mesh due to voltage sources. This shortcut procedure is a consequence of selecting all the mesh currents in the same direction and writing KVL as each mesh is traversed in the direction of its mesh current. Of course, the shortcut method applies only when no sources are present except independent voltage sources.