To add the vectors $(2, 3)$ and $(4, -1)$, you need to sum their corresponding components, resulting in the vector $(6, 2)$.

When adding vectors, you simply combine their respective components. Vectors are typically represented in the form $(x, y)$, where $x$ denotes the horizontal component and $y$ represents the vertical component. For the vectors $(2, 3)$ and $(4, -1)$, you will add the $x$-components together and the $y$-components together.

First, consider the $x$-components: $2$ and $4$. Adding these gives:

Next, examine the $y$-components: $3$ and $-1$. Combining these results in:

Thus, the resultant vector from adding $(2, 3)$ and $(4, -1)$ is $(6, 2)$.

This method is effective because vectors represent quantities that possess both magnitude and direction. By adding the corresponding components, you are essentially merging these quantities in a clear and organized manner. This process is akin to performing arithmetic addition but is carried out separately for each dimension (horizontal and vertical).

In summary, the process of adding vectors involves simply combining their corresponding components. For the vectors $(2, 3)$ and $(4, -1)$, the resulting vector is $(6, 2)$. This new vector encapsulates the combined effect of the original vectors in both horizontal and vertical directions.